I can think of several notable examples, including the Naval Mutiny of the Kriegsmarine in 1918 and the planned mutiny of the Black Sea Fleet in 1905, which eventually was carried out mostly just by the Battleship Potemkin. Yet while I'm sure that plenty of men in the Army also had sympathies with Socialist causes, if so, they certainly seem to be less notable in their expression of it. Even looking at the Russian Revolution, which the Army no doubt took part in, their participation seems to be fractured and without real direction early on, while the Navy, best exemplified by the Kronstadt Uprising, seem to have been much more dedicated to what they saw as their cause.
Modified from an earlier answer
Part I
The importance of sailors ashore in revolutionary activity in the first third of the twentieth century was certainly an oddity, and in the case of the Russian Revolution and Potmekin's mutiny, the subject of much celebration and selective commemoration. There was a similar overlap in the origins of for these naval mutinies, but there were some key differences between them as well. These differences reflected the divergent contexts, political cultures, and social hierarchies of both fleets.
In hindsight, Potemkin set a number of the patterns for later mutinies. Not only did it occur during an unpopular war, the Russo-Japanese War led to an enforced idleness that exacerbated preexisting tensions between the officers and sailors. Pay divides and social divisions between the upper and lower decks was quite severe. Added to this was the low quality of rations, famously immortalized in Eisenstein's Battleship Potemkin along with the enlisted-officer divide, that made it an explosive mixture. The combustibility of the situation mixed with those on land as strikes and other disturbances felt themselves on board. Some individual sailors, many of whom were drawn from Russia's nascent proletariat, had connections with various radical organizations. This gave the mutiny not only a ready-set of political leaders, but also primed the sailors' grievances to be framed in terms of contemporary politics. This was a pattern for other naval mutinies; while the bulk of mutineers' grievances were directly related to the conditions of their service, such grievances were conducive to being politicized.
In the case of the Russian Baltic Fleet in 1917, the immediate epicenter for its participation in the February Revolution was the cruiser Aurora in Petrograd and the large-scale mutiny at the naval base of Kronstadt. Dockworkers stormed the cruiser while she was refitting and lynched its captain and seriously injured its senior officer nearly a week after the Tsar's abdication. Simultaneous to this, the naval base at Kronstadt mutinied and murdered its senior officers, notably its commander Admiral Robert Viren. Although the sailors of Petrograd and Kronstadt did not produce any leaders in February, they did provide the Revolution much needed footsoldiers and access to military stores on the bases.
In hindsight, both 1917 mutinies and the swift evaporation of the Baltic Fleet command structure at Kronstadt were not surprising. Like its German counterpart, large portions of the fleet had spent a significant time rusting away at port. Rations in the Baltic Fleet were poor, and its officers elected to keep its men occupied with drill and various busywork. Viren in particular earned a reputation as a harsh martinet and drillmaster, but other Russian ships had significant numbers of disciplinarians among their officers. Kronstadt earned the nickname the "Sailors' Sakhalin" both because of their social isolation and the amount of punitive discipline meted out by Viren. Sailors' wages were poor and could not keep up with the wartime collapse of the economy.
But boredom, poor pay, and pointless military regimentation were far from the only elements contributing to this revolutionary tinderbox. There were several factors that were unique to the Russian context that made the fleet conducive to revolutionary action. Modern navies are complex entities and often draw from literate and skilled workforce for their recruits. The social picture of the Russian Navy's lower decks prior to 1914 was one of an increasing number of men drawn from a working class milieu. Kronstadt's position as a maintenance and training depot also meant that it had an above-average number of men drawn from the ranks of Russia's working classes. In an obverse picture from the army, only a quarter of the fleet came from the peasantry, with factory workers making up a third of the ratings, and various unskilled laborers the remainder. As such, the men were often exposed to various streams of radical Russian thought like the Socialist Revolutionaries (SRs) and the RSDLP (also known as the Bolsheviks and Mensheviks depending on your political faction). Although proactive measures enacted by officers like Viren tried to prevented the formation of large cells of revolutionary groups, these ideas percolated within the fleet. Enforced inactivity also allowed for a class of intellectuals within the fleet to emerge, and these figures would play a larger role in the October Revolution and Kronstadt Rebellion of 1921. The mutiny of the Potemkin in 1905 gave many of these incipient revolutionaries a script to follow and a model to emulate when the revolution came to the fleet. Potemkin also provided another salient lesson for revolutionaries. The Black Sea battleship's guns allowed it to assume a powerful position in the course of the Revolution, and in 1917 both the feet's guns and the arms at the base were of immediate utility to the Revolution. Even wartime nationalism played a role in radicalizing the fleet. While the fleet's ratings were drawn mostly from the Great Russian regions, its officer class was predominantly of Baltic German extraction. Wartime Germanophobia, which also cast aspersions on the Empress Alexandra, added to a gulf between the officers and men that only widened with the outbreak of revolution. News of Kronstadt spread to the active battlefleet, which had many of the same problems as the shore bases, and confusion among the officers as to who was in charge in Petrograd ceded initiative to the mutineers. The crews of the battleships Imperator Pavel I and Andrei Pervozvanny precipitated a general mutiny on 16 March and signaled the fleet's side in the Revolution.
The sailors' mutinies in Germany the following year followed a deceptively similar trajectory as their Russian counterparts. The large and medium surface ships of Kaiserlich Marine (KM) had been mostly confined to port after Jutland. Despite minor operations in the Baltic, and the occasional training sorties, the sailors of this moribund force had relatively little to do between 1917 and the 18. Although they were better fed than the rest of the civilian population, KM rations were increasingly lower quality. One of the common staples was sarcastically called Drahtverhau, a this soup one KM sailor described as 75% water, 10% sausage, and 6% vegetables, and 9% other. Officers often resorted to petty busywork and discipline to keep their men from being too idle, but while this strategy has its uses over the short-term, it was deleterious to their relationship with their men the longer it went on. Sitting idle at port also meant KM sailors came into contact with dockworkers and other laborers who were increasingly radicalized by news of the Russian Revolution as well as the increasing privations on the home front. The emergence of the Independent Socialist Party (USPD) among various working-class circles sharpened labor activism in the docks and other port facilities. Like the Russian Baltic Fleet, many of the KM enlisted men came from skilled working class families, so these connections with their dock workers were easy to accomplish. Sailor canteens became a source of political discussion, USPD literature circulated among sailors, as well as other pamphlets advocating radical political change.
By the summer of 1917, it was clear that some radicalization of the lower decks was apparent. In June 1917, the engine-room of dreadnought Prinzregent Luitpold went on a hunger strike demanding higher rations and an end to Drahtverhau. The Prinzregent Luitpold's officers gave in, and that in turn only stimulated more disturbances. On 5 July, Friederich der Grosse's enlisted men ate the next day's rations during coaling and threat of a hunger strike forced the officers to relent to the demands of the sailors to evade punishment and permission to form food supervisory committees. Many of the other ships' enlisted men followed suit and formed these organization, despite not receiving official permission.
By August 1917, the fleet was in a state of near-mutiny; when the officers cancelled the Prinzregent Luitpold stokers' leave and ordered the to report to shore for infantry training, the stokers simply deserted. When the officers put the stoker ringleaders under arrest, representatives from the sailor's councils of the other ships decided that the crew of Prinzregent Luitpold should stage a walkout. On 2 August, 600 men of the dreadnought left the ship. The officers of the KM managed to restore order by summoning a courts-martial and executing five ringleaders of the walkout. But in authorizing these executions, KM commander von Scheer denied the accused a chance to appeal their sentence to the Kaiser. Further regulations forbid political agitation by the USPD in the fleet and the KM officers further tightened discipline. One of the purposes of Operation Albion in the Baltic was to give the fleet something to do and restore the sailors' martial character by participation in a successful attack.
But the damage between enlisted and officers had been done and remained in place after the events of 1917. When the Kaiser visited the High Seas Fleet in October 1917, instead of the traditional "Hurrah", some sailors said "Hunger." The false dawn of Germany's military fortunes post-Brest-Litovsk staved off activism, but by the time it was apparent that Germany had lost in the West saw a renewal of activism within the fleet. In the fall of 1918, rumors circulated within the fleet of the imminent Operations Plan No. 19, a plan to bait the numerically superior British and American fleets around the North Sea island of Terschelling.