They started as the Dead End Kids, then they split into the Little Tough Guys and the East Side Kids, then finally becoming the Bowery Boys.
The Dead End Kids are probably the most well-known from the movies "Dead End" and "Angels With Dirty Faces". There were six kids in this group (and at this time, they were kids, the boys were in their early to late teens): Leo Gorcey, Huntz Hall, Billy Halop, Gabriel Dell, Bobby Jordan, and Bernard Punsley. This series had a run of 7 movies in the late 1930s ('37-'39) from Warner Bros.
Due to popular demand, the group was split, first into the Little Tough Guys (Hall, Halop, Dell, and Punsley). This series didn't fair too well as Universal Studios didn't use the best quality film. There were 9 movies and 3 serials made from 1938-43. This series is the toughest to find on home video, but the first movie "Little Tough Guys" and the 3 serials can be found.
While Universal was making Little Tough Guys movies, Monogram wanted to get in on the popularity and so the East Side Kids series was created. Halop was not in this series which lasted from 1940-45. There were 21 movies that starred Gorcey, Jordan, Hall (who joined the group on the 5th movie and became a mainstay), and Dell, with the rest of the group changing for nearly every movie. However, the first movie "The East Side Kids" didn't have any of the regulars. This series is the easiest to find the most movies on home video. It's debateable that this series was the most popular.
Debateable because the Bowery Boys has a sort of cult following as these films are hard to find new, but can be found and most of these were shown on TCM in the summer of 1999. This series had 48 movies and ran from 1946-58 (and the "boys" were no longer boys by this time!). These movies starred Gorcey and Hall (until Gorcey left due to his father's death in 1956--more on this later), Jordan remained through the first 8 movies, and Dell was in about half or so of the movies. Since Gorcey and Hall were considered the stars, when Gorcey left, Monogram/Allied Artists "replaced" him, mainly because Hall still had 7 movies left in his contract and Gorcey's absense would leave too much of a void (it did, anyway). To diehard Bowery Boys fans, the last 7 movies are considered to not be as good because they lacked the chemistry between Gorcey and Hall, but most of these fans will say they have seen them only because those last 7 were still technically Bowery Boys movies.
The Bowery Boys movies were mostly comedies (*slap*stick, mostly, with emphasis on the "slap" part) with the occasional dramatic overtone.
For those who may be wondering...
This is kind of a tough question considering the group changed several times, but the key players of the Bowery Boys series are...
Leo Gorcey as "Terrence Alouicious 'Slip' Mahoney" - Slip is most likely best known for his ability to "moider" the English language, first with his distinct New York accent and second with his ability to use the wrong words--malaprops--(ie: Slip would say "foist wit' his extinct New Yoik accent..."). He was the leader and the "brains" of the group.
Huntz Hall as "Horace DeBussy 'Sach' Jones" - Sach is most likely best known for being... well, Sach. Probably not the brightest (although he has his moments and quite a few of them at that), he always managed to get into trouble
rather than get out (ie: one movie saw Sach getting his tonsils removed, afterwards he had this amazing singing voice, but it later disappeared because he saw a doctor to get rid of the "tickle" in his throat). He was the type of guy everyone would want as their friend.
Gabriel Dell as "Gabe Moreno" - Gabe appeared in about half of the movies, but never in the same line of work. He seemed to always be one step outside of the group.
Bernard Gorcey (Leo and David's father) as "Louie Dumbrowski" - Louie ran the boys' hangout, Louie's Sweet Shop. For some reason, Louie let the boys owe him for all the banana splits they ordered... even though he was never paid for them. Unfortunately, in 1956, Bernard was in a car accident and died, which caused Leo to imbibe even more than he already did. Eventually, just being on the movie set became too much for Leo and he left the movies.
David Gorcey (Leo's brother) as "Chuck Anderson" - Even though Chuck was always in the background, he appeared in every movie except the first one.
The rest of the group (which changed every so often) consisted of:
Bobby Jordan as "Bobby"
Billy Benedict as "Whitey"
Bennie Bartlett as "Butch"
In the later movies, more groups members were introduced as we soon saw the above 3 leave. A side note, there were actually 2 Butch's in this series!
When Leo Gorcey left, Monogram replaced him with Stanley Clements, known as "Duke" in the last 7 movies. Clements was not new to the group, he'd been in a few of the East Side Kids films as one of "the rest of the group."