I can only speak for myself; I personally like the American accent; my girlfriend is Californian, in fact, and I love her accent (but I would say that, wouldn't I!) Midwestern accents I quite like; they sound almost Irish to me, sometimes. I find Southern US accents sound a little funny...I guess I kind of associate that accent with stereotypical rednecks, which is unfortunate because I'm sure most Southerners are not that way at all, but there you go. I've been watching a lot of The Sopranos recently and the New Jersey accent is really growing on me; it's quite a tough accent to imitate properly, too. Oh and the Bostonian accent (which I only grew really familiar with in the Scorcese movie, The Departed) is really hilarious to me.
In general though, I like the standard American accent; it's quite pleasing to the ears, though one issue I have is, like, how some Americans, like, use the word 'like' about five times every, like, sentence. Most use much better English than British people, though. I don't agree with the common British tendency to see Americans as bastardizing our language; Americans are nearly always much more eloquent speakers, and have far better spelling and punctuation than the British, who are frankly dire at these aspects, for the most part.
Hope that helps!