The Allies had large submarine forces in both World Wars. They're less well known than their enemies, simply because there was less for them to do. In the European theatres of both World Wars, they were facing a continental power, which had no need to import food and resources and so offered few submarine targets.

In the First World War, Britain entered with a large submarine force, albeit one with a large amount of obsolete vessels. The main submarine class used was the E class, one of the more modern submarine classes in use at the time. They would prove highly useful in assisting the blockade of Germany. They also found employment in the Dardanelles campaign, with the obsolete Turkish battleship Mesudiye being sunk by the equally obsolete HMS B11. RN and RAN subs operated in Ottoman waters from 1914-1918, sinking ships and shelling the coast. Five VCs would be awarded to submariners during WW1. British subs would also be deployed to the Baltic to blockade the sea routes between Sweden and Germany.

During the Second World War, the RN made extensive use of submarines in the Mediterranean, the Pacific and the North Sea. Operating from Malta, RN submarines seriously threatened German and Italian supplies to North Africa. They were used to land secret agents and commando teams, to shell coastal installations and to collect intelligence. British submarines also interdicted German convoy routes to Norway. On one of these patrols, HMS Venturer became the only submarine to torpedo another while both were submerged. The US navy submarine service went through a long period of teething trouble. The mk 14 torpedo they were issued with was almost completely useless for the first two years of the war. It had poor depth keeping, and an exploder which didn't work. Once these problems were fixed, they were instrumental in stopping shipments of food, rubber and oil to Japan. Towards the end of the war, the Japanese fleet was all but confined to port due to fuel shortages caused by the sub blockade. Submarines sunk several major warships, including the carriers Taiho and Shinano.

Sources

Rising Sun, John Toland

Churchill's Navy, Brian Lavery

Castles Of Steel, Robert K Massie

While I know the Allies had subs in WWI and in the Atlantic in WWII, my personal specialization is WWII in the Pacific, so I'll speak to that.

The US Navy strangled the Japanese with submarines. Throughout the entire Pacific War, Japan lost some 8.1 million tons of merchant shipping. 4.9 million tons of that amount, roughly 60% of the total, was caused by submarines. Further, eight Japanese aircraft carriers, 1 battleship, and 11 cruisers were sunk by US subs. See here for an official US Navy history on these numbers.

Just four days after the attack on Pearl Harbor, the USS Gudgeon (SS-211) left Hawaii for a patrol in Japanese waters. 23 other patrols left Pearl over the next four months. These patrols sunk 18 freighters and the Japanese sub I-173 (by Gudgeon).

By the end of the war, the US Navy had lost 52 submarines and 3506 crewmen in the Pacific. But the submarine force as a whole strangled Japan economically and militarily.

Some excellent responses already, but just to emphasize, the single most effective submarine campaign in history was the USN's strangling Japan of resources, and destruction of her merchant marine, which until very late int he war was virtually all done by the sub fleet.