Indeed, out of my survey of chanties attributed to the time period up through the 1880s (i.e. the life of chanties in their prime), this one, "Mister Stormalong," turns up 21 times. (In the extended survey, into the 1920, it turns up 32 times.) Alone it is the 9th most commonly evidence chanty in my research. If I were to factor in the other "Stormalong"-themed chanties, they would total as the most common of all chanties to be noted in history. In the Revival era, they certainly have not been unknown; this specific form, Mr. Stormalong, is probably the best known. However, neither is it terribly popular, either—at least not in recent years. The song actually presents the possibility for a short narrative, too. Nonetheless, I'm not sure why it is not more popular among singers nowadays.
When I visited Liverpool in 2009 I had the opportunity to sing some chanties on stage in a bar. In choosing repertoire, I thought first that I'd pay tribute to my hosts with some Liverpool-associated songs, like "Blow the Man Down." However, during my visit I felt like I was getting a bit of a vibe off people like "We are Scousers and we are more familiar with chanties than you ever will be!" Ha! Maybe I was imagining it. Though I thought it funny that the Maritime Museum wasn't selling Hugill's Shanties from the Seven Seas, nor any other chanty books or recordings. I thought that instead of confirming their expectations by giving what they might know, give them something "from America" that was unfamiliar: a set of all "Stormalong" chanties (along with "Old Moke").
In any case, you may have guessed that I am personally fond of the Stormalong chanties!
This particular, pump style chanty, Mister Stormalong, actually doesn't turn up in the historical record until a bit later than some of the other ones. But once it does, it was popular in the collections. The first confirmed publication with it is Alden's famous 1882 Harper's article. Alden said this about it:
Here is another “Stormy” song that contains a hint of negro origin in the word “massa,” and suggests that perhaps the legend of “Stormy” is an African rather than a nautical myth:
Old Stormy he was a bully old man.
To me way you storm along.
Old Stormy he was a bully old man.
Fi-i-i, massa, storm along.
The song's existence earlier than this publication is suggested as early as 1856, in the memoirs of Gen. William Jackson Palmer (Fisher, A Builder of the West, 1981). John Short, who sang for Cecil Sharp, started his sea career a year or two later, and ended it in the mid-1870s, so his memory of the songs also suggests it was around by the mid-1850s. Capt. Whall probably learned it circa 1862/3. The combined testimony of many others makes it fairly certain that it was very common amongst the chanties of the 1870s.
After Alden, Luce had a verse in his 1882 work and Davis and Tozer included a fully fleshed out version in their 1887 collection. Hugill's presentation made much use of the latter. From the beginning of the project, I would pick and choose which verses I felt like singing from amongst those offered by Hugill (later, I started to make my own). So whatever I have here certainly won't match.
An interesting footnote is that the composer Percy Grainger participated in collecting an interpretation of "Mister Stormalong", from John Perring in 1908, and noted another sung to him by Charles Rosher in 1906. In 1907, Grainger composed a concert music arrangement of the song, published circa 1922/3.
A bit of Grainger's arrangement can be sample here.