Californication is great. Weeds too, also on Showtime, although it has slipped a bit in recent seasons.
Most of the HBO series are good. Back in the day I loved Six Feet Under. These days I'm enjoying Big Love.
I like House too, when it is on. It seems to go on Hiatus an awful lot, doesn't it? Friday Night Lights, about small town Texas high school football, is another favorite show of mine -- it is amazingly well and gets a lot of critical acclaim, but the ratings have never been good enough to keep it from the brink of extinction. There are also a few family dramas like Brothers and Sisters that I watch, although Brothers and Sisters is not nearly as good as it once was.
As for ones to use in class ... my students loooooove Gossip Girl, this show about rich Manhattan teenagers. Maybe it is because they feel like they're watching their American counterparts!