I'm just going to list the American Drama's I like that I've been watching on TV.
Dexter. (A serial killer who's also a forensic expert for the Miami Police Department, a different storyline each season)
Big Love. (A finished series about a family of Polygamist Mormon's trying to succeed at business in Utah, while keeping their family safe. Features Bill Paxton.)
Six Feet Under. (A finished series about a family and their individual problems, while they try to keep their family run Funeral Home business running, while under challenge by a large corporate Funeral Home company. Features Michael C. Hall, who plays Dexter in Dexter.)
Game of Thrones. (The HBO version of George R.R Martin's hit book series, A Song Of Ice And Fire. A really good series that follows very well to the original story. Features Sean Bean, who played Boromir in Lord Of The Rings.)
If you're a fan of sci-fi Drama, then Doctor Who and Torchwood are good series.
Doctor Who is brilliant, and Torchwood is a more adult spin-off of Doctor Who.
If watching Torchwood, expect to occasionally see John Barrowmen kissing other men.
But, watch out for that happening in Six Feet Under, also.