Since you mentioned Adium, I can deduce that you're running Mac OS X, and you're absolutely right, the AIM application for the Mac is not exactly the most thrilling program, but, to be fair, as a simple IM app, it is pretty good. (make sure you have the latest version, btw: it's improved HUGELY in the last year or so).

Adium, on the other hand, is still pretty darn cool: I use it too, and I love having a single app that works with AIM, Yahoo's YIM, MSN, Gtalk, and more. One app to rule them all. Except... except it doesn't appear to properly block people when they bug you on AIM.

Fortunately, it's not too painful to just launch the AIM application itself and use it to tweak your own privacy settings, and that's what I'll demonstrate. Don't have the latest version? You can download AIM for Mac OS X easily enough.

Okay, so, step one:

Choose Preferences... and you'll see this:

Not quite what we want: click on "Privacy" along the top. Now you're in the right spot:

The key here are the three choices under "Who can contact me?" I strongly suggest that you change it to the setting "Allow only users on my Buddy List". Make that change, then just close the window (I kinda wish there was an "Okay" or "Apply" button from a usability perspective, but that's another story).

Now you should be shielded from the jerks and weirdoes on AIM. Well, other than those that you're already friends with! :-)