I think it can be said that Boba Fett captured people's imaginations. It should be noted that he always had a decent amount of backstory when you look at the original "Star Wars" novels which explained some of the concepts. Simply put Jedi are presented as Super Human and almost unstoppable, however Boba Fett was a relatively normal human who with weapons and training could fight them on fairly equal terms.
As a result you find that in Star Wars people tend to either want to be a Jedi, or a character who for whatever reason is equal to one, and the Boba Fett/Bounty Hunter thing is what opened that door within the Canon. Graned Boba Fett *DID* sort of get robbed in the movies, but in part because it was meant to be a quick thing, and the movies missed some of the subtext of pointing out things like how Luke Skywalker only survived fighting him because of what amounted to dumb luck. The rope he used was a "Smartrope" and was proof against being cut by Lightsabers, being a weapon designed for use on Jedi, however one of the idiot thugs fired allowing Luke to free himself with a deflected blaster bolt.
I think Boba Fett started out as a cult character for those who knew what he was about, but as the universe became more expanded for the mainstream more people gained an appreciation for him.
I also tend to think part of the appeal is his existance as a sort of neutral party. He really has no motivations revolving around absolute good or evil, he hunts down people other people are willing to pay for. He's a "villain" in the storyline, but really he's not a bad guy and probably spends most of his time hunting people far worse than he is.
One of the things that always kind of irked me about most games based around Star Wars, whether they be PnP games or Video games, is that when Bounty Hunters show up they are automatically defined as being evil because Darth Vader hired them in the movies/books, when actually they shouldn't, being more neutral, or even good since while Boba Fett did do some work for the underworld (hunting criminals for other criminals) many probably just go after whomever the goverment puts a bounty on.
Interestingly I find it somewhat lulzworthy that such material tends to mark Smugglers as good guys, because Han Solo was one. Oddly Smugglers (including Han) are basically runners of drugs and slaves. Han got into trouble because he ONLY ran drugs/spice and refused to run slaves and freed a cargo full he picked up from Jabba when he figured out what it was. Strictly speaking Boba Fett and Han Solo representing exceptions to the general "alignment" of their profession if there ever was one. This being one of the things that kind of irks me about the upcoming "Old Republic Online" in fact.
At any rate, enough rambling. The point is that Boba Fett is cool, he was conveyed well through attitude (which got attention) and had a neat costume for the movies.