"Classic" or "Aristotelian" trolling is a form of full-contact satire. People object to it because it's annoying, but then again that's the point. The object of trolling is to generate amusing and (hopefully) intelligent chaos.

There's more than one kind of troll.
  1. Political trolls. Political trolls are all about bad logic and cognitive dissonance. Ideally, parts of the troll should grind against each other so badly that readers are faced with a serious ontological clusterfuck. In practice that's not always easy, and it's always a fun consolation prize if some third party starts defending the troll out of sincere convictions. You meet some really scary people that way -- or are they just co-trolling? It's all part of the fun!

    1. The Right Wing Maniac (RWM), with whom we may be familiar; these can be blatant or relatively plausible. The relatively plausible ones are often hard to differentiate from sincere people why may or may not have issues.

    2. The Left Wing Maniac (LWM) is, for some reason, less common. Successful LWM riffs on Slashdot include: The radical notion that women are people (always a winner!); any suggestion in favor of "big government" -- or any attack on any adolescent libertarian shibboleth; anti-Americanism. These ideas strike me as less maniacal than common-sensical, but on Slashdot they're viewed as full-bore insanity, so how can I complain?

  2. Perl

  3. Surrealism: The original Natalie Portman troll is a classic and frequently brilliant surrealist troll; the cheap imitations are boring.

  4. Social Commentary: At the risk of nodevertising, may I offer my own Nodevertising Metanode as a handy (albeit poor) example. MEEPT!!ian social commentary is, like, social commentary but much funnier.

  5. Cretinism: In the last few months, Slashdot has been plagued with idiots who post obscene one-liners and copy'n'paste crap. For some reason, these critters get called trolls. It's depressing. (update 4/16/00: We've seen a few of them here recently, too. Just ignore them, like sensei says.)