There are alot of TV-series out there. Ive got my own list of which I watch and would recommend.
How I Met Your Mother
A fantastic and entertaining series about a couple of friends living in New York. Kind of "Friends" like, but different. The story is based on the main caracter "Tedd", in the future telling his kid about how he met their mother. It has stunning caracters, especialle "Barney", the "awsome" guy who also has a popular meme these days. This is a series you MUST WATCH.
The Big Bang Theory
A hillarous series about some "nerds" living in LA. A preety girl named Penny moves in the same block, and you follow their lives. Amazing humor, especially with the caracter "Sheldon" which is very intelligent but without many social skills. Can seems very nerdy, but is in fact very entertaining.
The Walking Dead
A pretty new series I think, based on a Zombie Apacolypse. This is a more serious, and exciting series based on some main characters and their life during the infection. Many horror scenes, and long episodes. You will get addicted and be hungering for the next episode.