First off, I don't consider most of these self-proclaimed hackers to be hackers at all. Most are teenagers, ranging from 13 up to about 18, 19. After that, they grow out of immaturity.
The media created two groups of hackers: the evil ones, known as Black Hat hackers, who break into systems and trash it (see 2600's Hacked Archives for examples), and the group of older wiser genius programmers, White Hat hackers, who can take a Apple IIe and turn it into a coffee machine. I consider both groups geniuses in their seperate ways. Which is the group that deserves the title? Depends on who you ask.
The "hackers" of AOL are largely male teenagers who wish to annoy other persons. To pick on weaker persons. They have little to no skills or experience in computing. Since they don't have advanced computer intellegence, they try to make up for it in cunning and deception. This usually means they pretend to be someone else and make up stories to try to get passwords to other accounts. (Black hats call it social engineering)
Some pick up some knowledge of a programming language called Visual Basic (VB) to create programs. These programs are used to harass other users, through chat rooms, Instant Messages (IMs, like real time email), and email. Programs, called 'punters', send HTML tags through IMs to crash certain AOL clients. The latest version of AOL, AOL 4.0 for Windows, that was just released is not immune to such attacks as claimed.
So, how do these kids manage to bypass AOL's security? They don't, really. They use their only true skill, lying. They usually can call up a Billing Representive and claim to be the owner of an account they want to comprimise. If that doesn't work, there are plenty of AOL employees who don't care if they break AOL's rules. Would you if you're being paid $7/hour?
AOL employees have been known to release information, harass (or stalk) members, reset passwords, and many other things. AOL management ignores it, as if overlooking a problem would make it go away.
Ok, I'm done ranting. That pretty much sums up AOL "hackers" and what they do....