In short, the various Allied nations did utilize Submarine fleets in an unrestricted campaigns against the Axis Powers during World War Two. The Americans, the British, and Soviets all used Submarines in a variety of capacities in that war. As my focus is on the First, rather than the Second World War, there will be plenty of space for another user to tackle submarine usage in World War Two.

My answer will, instead, focus on the the usage of submarines by the Allies during the First World War, and touch on the unrestricted campaigns run by the Germans.

Germany was actually fairly late in developing a submarine arm. Other nations such as France and Spain had been testing submarines throughout the late 19th century, and during the 1890s truly workable military submarines had been designed (most notably by John Holland, residing in the United States).^1 The United States adopted submarines in 1900, with the Royal Navy adopting them the following year. The first German submarine wasn't ready until 1906. So, the question of other countries adopting submarines isn’t the most productive one, as they had mostly done so before the Germans did.

Now this brings us to the war itself. Submarines had proved useful to most Naval powers at the time. For example, among the first units of the Royal Navy to start war operations in 1914 were British Submarines sent to perform reconnaissance within the Helgioland Bight against the Germans.^2 The French, Italians, and British operated submarines in the Mediterranean and Adriatic Seas. The British and Russians operated submarines in the Baltic Sea. The British and French operated submarines in the Sea of Marmara, while the Russians operated submarines in the Black Sea. The Americans would eventually operate submarines based out of the Azores Islands, Ireland, and the American East Coast.

For the most part, what differentiated the submarines of the Central Powers from the submarines of the Allies were the kinds of operations they were used for. In the Allied anti-shipping campaigns, they attempted to utilize their submarines in a manner that reflected the “cruiser rules” of prize warfare. They would attempt to board Central Power ships and check their cargo, before deciding to either inter, sink, or let the vessel go. This is in comparison to the Central Powers who utilized an “unrestricted submarine campaign” which meant that vessels were liable to be sunk without warning, either by torpedo or deck gun.

This is a pretty major difference. In some respects, an unrestricted campaign would be more successful than a restricted. However, you can not discount the effect that Allied submarines had on Central Power shipping and trade. For example, the campaign in the Sea of Marmara had a major effect on Ottoman supply lines during the Battle of Gallipoli and the citizens of Constantinople/Istanbul. While the Allies never completely shut down sea-borne transport lines, the Ottoman military shifted to a primarily land based route which wore down Ottoman troops involved in the long marches, and it additionally tied up transport vehicles to the Gallipoli front, negatively impacting their operations in other theaters such as the Caucasus or Palestine fronts. This, in many ways, can be read as a success by Allied submariners.^3

1915 and the Sea of Marmara did not see the only successes from Allied submariners. Central Powers shipping in the Baltic Sea was also disrupted, with, in the words of Norman Polmar,^4

In the Baltic, reinforced by British submarines, the Russian submarines had a substantial impact on the freedom of operation of the superior German fleet and seriously disrupted German merchant traffic, necessitating substantial reallocation of German naval resources to that theatre.

Polmar is referencing, in part, the adoption of convoying by Central Powers ships in 1916 in the Baltic Sea as one way of protecting themselves from submarines. In 1916 the Allies did not sink any Central Powers vessel that was in a convoy. In the Black Sea, the Russians were able to almost entirely halt the Ottoman coastal trade with their submarines. So it’s safe to say that as an anti-shipping weapon, the Allies had a generally good handle on their submarines. Of course, the submarine never became the weapon of an economic war for the Allies as they were relying primarily on a surface blockade, enforced primarily by the Royal Navy.

The Allies did not limit their submarine usage to anti-shipping campaigns. As I hinted at earlier, the Allies were using their submarines for reconnaissance and in an anti-submarine role, a forerunner to today’s “Hunter-Killer” submarines and tactics. In the North Sea, American and British submarines would be sent on patrol billets where they would be on the lookout for German U-Boats. These patrols were long and tedious, and in many cases did not result in sightings.^5 In the Adriatic Sea, the Italians and French used their submarines to attempt to raid Austro-Hungarian harbors and to sink Austro-Hungarian submarines.^6 None the less, the presence of Allied submarines was feared by both German submariners and German admirals. Submarines acted as one deterrent against the High Seas Fleet sallying out against the Allies, and German submariners were afraid that they too could be torpedoed at any moment. The presence of Allied submarines often caused the Germans to attempt to patrol in different areas with less Allied activity.

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Finally, I’d like to tackle another assumption present in your question: The success of the German submarines during the First World War. There are two primary ways I think that this can be measured. Firstly, did they achieve their stated goals? Secondly, did they pose a credible threat to the Allies?

On the first question they did not achieve their stated goals. The Germans intended to use the submarine in order to starve the United Kingdom into submission to sue for peace. This goal was lofty and I discuss the decision to launch the unrestricted campaigns here. However, while they may not have achieved their stated goals, they did pose a credible threat to the Allies in which the Allies had to respond. The second unrestricted campaign led to the introduction of convoys and a major shifting of naval forces. Even the Japanese pitched in and sent destroyers to the Mediterranean. So, when qualifying the German submarine campaigns, it’s best to keep in mind that they did not achieve their ultimate goal but were a threat.

If you'd like to read some more about Allied submarine operations during the First World War, I have written about the Americans here, and the Allies more broadly here.

Sources:

• 1: Some resources on American submarine development include U.S. Submarines Through 1945: An Illustrated Design History by Norman Freidman, The American Submarine by Norman Polmar, and Building American Submarines 1914-1940 by Gary E. Weir.

• 2: British Submarines At War: 1914-1918 by Edwyn Gray provides a good starting overview of British operations during the war, although it's focus is more on the "exciting" events.

• 3: Evren Mercan (2017) The impact of Allied submarine operations on Ottoman decision-making during the Gallipoli campaign, Journal for Maritime Research, 19:1, 63-75, DOI: 10.1080/21533369.2017.1357949

• 4: Norman Polmar, Submarines of the Russian and Soviet Navies, 1718-1990, page 63.

• 5: As of current, the only secondary source on American submarine operations is: Caroll Storrs Alden, "American Submarine Operations in the War", Naval Institute Proceedings, Volume 46/6/208, June 1920 and Caroll Storrs Alden, "American Submarine Operations in the War (Concluded)", Naval Institute Proceedings, Volume 46/7/209, July 1920. Subsequent works on the subject have exclusively drawn from these two papers.

• 6: A good account of Anti-Submarine Warfare is Dwight R. Messimer, Find and Destroy: Antisubmarine Warfare in World War I.

If you're interested in reading about this topic in depth, I would recommend War Beneath the Sea, by Padfield. It's a fairly exhaustive single volume book that examines the development, doctrine, and performance of submarine fleets for all of the major powers who fought in WW II.

I think the German submarine force gets so much focus because 1) it was indeed very good, but 2) there wasn't much going on with the German surface fleet in WW II. Outside of some commerce raiding of little strategic impact and a couple of well known engagements (Bismark), the RN successfully maintained naval dominance above the waves. Towards the end of course Germany disbanded many of its surface units and reformed them into new infantry divisions, which tells you how unimportant the German surface fleet had become. It was the submarine force that had an actual strategic impact on the war, therefore it gets a lot of publicity (much of it deserved).

The British invested heavily in submarines prior to WW II (though their designs left something to be desired), but the story of the Royal Navy in WW II is so much broader than the submarine fleet. And of course the British submarine fleet could hardly be strategically decisive against a foe like Germany (although they had plenty of action and success against the Italians in the Med.).

The US similarly invested heavily in submarines, and arguably built the best submarines of any major nation of WW II (although regrettably, with some of the worst torpedoes). Large and technologically advanced submarines with good range and important quality of life features like air conditioning that allowed them to have great endurance, important for a nation that had to cover vast distances in the Atlantic and Pacific. And of course US submarines arguably had the most decisive strategic impact of any sub fleet of the war, almost single handedly bringing Japanese shipping to its knees. But again, the story of the USN in WW II is much bigger than just the submarine fleet, so it doesn't stand alone as much as the German story.

As others have mentioned, other powers did in fact invest in submarines; in particular, the US submarine campaign against Japanese merchant shipping was immensely successful and a big part of the reason the Home Islands were so badly supplied in 1945 - recall that the Japanese still controlled large parts of China, but they couldn't ship the rice across to feed their home front. In "Embracing Defeat", John Dower relates how, after the war ended, rationing in Japan was still so strict that a judge, feeling he had to uphold the law in his personal life, literally starved to death trying to live on his official ration; that tells you something about how badly the Japanese merchant marine, on which their imports presumably depended, had been hit.

However, I would raise a point which neither of the two previous answers mentioned (perhaps thinking it too obvious): Submarine warfare is the weapon of the weaker power. A navy that has the ability to send cruisers to patrol their enemy's lines of communications doesn't need to bother with submarines; a heavy cruiser - much less a battleship! - can sink or capture a whole convoy in an hour's gunnery. By contrast, even the most disastrous (for the Allies) convoy battles of WWII were drawn-out attritional affairs where a good fraction of the convoy always got through. Consider SC7, for example, in October 1940: No air cover, escorted by only a single small warship, and attacked by a wolfpack of 7 U-boats. This convoy lost 20 of its 35 ships; it was perhaps the worst convoy battle of the whole war (the other obvious candidate is PQ17, 23 ships sunk of 34). And still, 15 ships did reach England! Tirpitz, or even Scharnhorst, would have sunk, or worse captured, the whole lot, because there's no way for the slow merchant ships to get out of range of those heavy guns before they're hit - and since they know that perfectly well, they'll surrender.

This is why the Bismarck and the Tirpitz could affect the whole deployment of the Royal Navy's battleships, and why the threat of a "breakout into the Atlantic" loomed so large in the operations of the Royal Navy until they were both sunk. An enemy battleship on the loose in the Atlantic threatened their whole trade in a way that almost no amount of submarines could do. In his history of the war, Churchill mentions the possibility that they'd have to provide a battleship escort to every convoy, to fight the Tirpitz on reasonably even terms; you can imagine the strain that would have put on their operations.

So one reason the British didn't build a large submarine fleet for purposes of commerce raiding (they did build a medium-sized one for operations against enemy warships) was that they had no need to: They could put six cruisers in the British Channel and a dozen patrolling the North Sea, and boom, Germany can't import anything by ship any more. (Exceptions for coastal traffic along Norway, and across the Baltic from Finland and Sweden - the cruisers can't go there, whether because of mines and land-based aircraft, or because they can't get through the Sound). No need for submarines - there's no targets for them!

A digression: The US was not "the weaker power" overall in the Pacific against Japan; but they were locally weaker in the seas surrounding the Home Islands. It would be quite late in the war before an American task force could get into those bodies of water. So for that specific part of the sea, the Americans used commerce raiding, and very successfully too.

This discussion is not specific to submarines; it goes back to the guerre de course and jeune ecole (respectively "commerce warfare" and "young school") concepts of the nineteenth century, and arguably to privateering and commerce raiding in the Franco-English wars from Westphalia to Napoleon. As you can perhaps tell from the names, these concepts arose in the French navy, discussing how they could overcome what was by then the apparently invincible dominance of the Royal Navy. The French were resigned to having fewer battleships, and being unable to gain a traditional command of the sea by just smashing the enemy fleet in a decisive battle, and then having the ability to send their cruisers wherever they wanted. (Conversely, this is the scenario that the Royal Navy always worried the most about, and the consensus on their side was that if they ever lost command of the sea in this way, they would have to make "peace on whatever terms we can get" - Sir Julian Corbett expresses that view in "Some Principles of Maritime Strategy", for example.) So the "jeune ecole" was the view that the French should instead build a large number of small, fast raiding ships, able to run away from a British cruiser, but heavily enough armed to smash up a convoy escort and the convoy. The French Navy never did get enough funding to build that fleet, but you can see that it's basically the same concept as building a large number of submarines that can hide from a cruiser. Either way it is the weapon of a power that can't afford a big enough navy to fight a decisive battle and gain the ability to put cruisers on arbitrary sea lanes; it's the oceanic equivalent of guerilla warfare - you run away from big enemy armies, and strike where they are weak.

So, to summarise: The victor powers of WWI did not invest heavily in submarines for commerce raiding because they expected to have command of the sea in the next war. They felt no need for a "guerrilla" force to deny use of the sea lanes to their enemies, when their "regular" (ie surface) navies expected to easily control them - and were largely correct in that expectation; there were no convoys running into German-controlled ports.