Series I would definitely recommend to anyone:
The Walking Dead - has a bit of added drama which it could do without it, but the good bits are really good.
Battlestar Gallactica - I originally thought it would be like Star Trek and I would hate it, but I really enjoyed it.
The Sopranos - fantastic show.
The Wire - Takes a bit of getting into, but once I did I could not put it down. Give it at least 2-3 eps to see if you like it.
Game of Thrones - I really loved the books and the show is very good. New season just started.
24 - Truly epic undertaking, not to be taken lightly!
Rome - Awesome show imo
Spartacus - bit over the top but some really good moments.
The Big Bang Theory - lighthearted comedy/sitcom with a hot blonde and some nerds, the hot blonde makes it worth watching alone tbh. Nice short eps.
The Inbetweeners - really enjoyed this, comedy gold.
The IT Crowd - how it feels to work in IT. "Have you tried turning it off and on again?".
True Blood - I enjoyed the first 2 seasons the most. After that i've kind've gone off it a little but I may step back in and watch Season 4 at some point.
Prison Break - Season 1 is a must. Season 2 is OK. After that I wouldn't really bother. Though Season 1-2 are worth watching anyway.
Dead Like Me - Show about a girl who dies and becomes a reaper. I thought it was pretty good. Got cancelled in the end though.
Band of Brothers - If you've not seen this watch it now!
Breaking Bad - You mentioned this but including it in this list for completion.
Dexter - You mentioned this but including it in this list for completion.
Death Note - A manga based series about a guy who finds a note book that lets you kill anyone by writing their name in it.
Bleach - Another manga based series, good main story line when you take out the filler episodes, these are best ignored.
Sadly i've pretty much seen all of the above. Getting hard to find good new shows to watch now.