I like my own accent well enough, which is Kyushu Japanese, but other Japanese people often make fun of me for it. Among Japanese accents, I love the Kyoto dialect. You could say it is like our version of a posh British accent- it is very polite, proper, elegant and almost archaic in the pattern of speech. Outside of my own nation, I love Russian, Middle Eastern, French, Greek, Irish... Actually, there are few accents I don't like. My favourites, though, would have to be Russian, Middle Eastern and Native American.
Russians have such a depth to their voices, and the language can paradoxically sound fluid and harsh at the same time. I actually took the time to become fluent in Russian, but my accent is pretty awful- Japanese+Russian is not a beautiful mix. I also know a bit of Arabic, Farsi and Turkish, as my partner is from Turkey. I love it when he speaks, I could listen to him all day. As for Native American... I cannot really describe it, but it is distinct and I find it very alluring, no matter what region the person comes from.
As for what I don't like, I cannot stand some American accents, namely that weird southern drawl that uses broken words and slurred syllables (what I suppose you could call "hick"). It is so hard for me to understand what the hell they are saying- It doesn't even sound like English!
