Most Simpsons characters are lazy comedy, there's some great writing in there (aside from the recent series..) but the characters are hardly well rounded. Pretty much everybody is an example of a stereotype and designed to generate cheap laughs.
Not everything in comedy has to be clever, sometimes it can just be light hearted fun. I think somebody mentioned Manuel from Fawlty Towers earlier, a pretty nailed on example of a stereotype .. and it was funny to a lot of people. I don't think people are watching the likes of the Simpsons, Family Guy or South Park for their intellectually stimulating content. It's cheap laughs.
I found Apu pretty funny, so did a lot of people I'd guess. I also completely disagree that he was a 'tedious character' @Halftrack .. I actually thought he was pretty good and represented as being a genuinely good, family guy, and I enjoyed his episodes. I've even seen plenty of people from India coming out and saying they found the character funny and don't understand the backlash.
I just hope this isn't a sign of the future of comedy, I think this is what a lot of people are worried about. At what point do the likes of South Park also start coming under siege from those who see themselves as being the comedy crusaders?
Are you actually going to miss him being in the Simpsons when you watch it though?