Dude, NObody likes what I like, but hey, you never know.
"Fly" - Lamb - Slow techno or something? I don't know or care about genre. There are a lot of electronic background parts and a chick singing, that basically makes it techno in my book. ;P Somebody make a video for this song, it deserves one... heh.
"Sometimes (Lester Piggott)" - James - Alternative. One of the best lyrics I've ever heard. Gorgeous song.
"Post-Modern Sleaze" - Sneaker Pimps - Again, I don't know. Sounds like it's from the same basic field as Lamb, but more subdued. Great story-song about a very common type of person...the singer's vocals are quirky, but I've always liked them.
If you can find it, I'll throw in "Ice Machine" by Depeche Mode, which is early-80s electronic pop. It was only on the UK release of their first album. I have a strange fixation with this song. Not sure why.
"Disappointed" - Morrissey. Subdued pop. You know I had to throw one of those in, of <i>course</i>... If you can't find that, try "Everyday Is Like Sunday" (one of my favorite songs EVAR!!!1) or for a quick and emotional one, "Angel, Angel, Down We Go Together".
That's five, that's enough. I actually will try some of the ones in this thread that don't sound like disposable trendy pop.

(and yes, I consider J-pop a trend.)