I don't mean the general requests that many people do, sticking a little message on their site somewhere that says "by the way, I LOVE getting fanart", because that's their site and they are allowed to do so.
But when people message you and say "Hey, if you ever get bored, you could always give us some fanart"...
One time, it's a bad, cheesy plea and/or lousy attempt at humor.
Twice, it's rude and obnoxious.
Three times, I make a note to never go near their comic again, much less draw them fanart.
Something about having to ask for people to show appreciation for your work irks me beyond belief. The whole concept of fanart is based on the idea that someone loved what you have created enough to attempt to fashion something in it's image. It is then presented to you as a sort of offering. Receiving fan art/fic/whatever-the-hell people make you (one nice person made me a banner when I had none) tells you that at least one person thinks you're doing something right.
When you have to ask for fanart, it is time to seriously rethink what the hell you're doing with your comic.
This is a lot like what I saw people doing on Elfwood and what I see now on DeviantArt. People's comments consisting of: "hey-nice-pics, PLZ COM LOOK AT MY ART N LEVE COMMENTS KTHX". Okay, I exaggerate. But when most of your comment is a plea for people to go look at your own work... why are you even commenting? Art galleries with systems set up to allow comments are so you can voice opinions and critiques of the work. Not whore yourself out. If you want comments, have the decency to attract people's attention by making them WANT to see what you've done - leave thoughtful, helpful, and honest comments. If you like something, try to say why. If you see something needing improvement, suggest what might fix it.
Similarly, people who wander into communities and say: "ADD ME TO YOUR FRIENDS LIST!" are rarely interesting enough to warrant adding.
I think I'm done bitching, now.