AMC puts out the best series on television, in my estimation. You can't go wrong with "Mad Men," Breaking Bad," or (as you noticed) "The Walking Dead." I missed the first couple of seasons of both MM and BB because I didn't think I was interested in either ad execs of the early '60s or in chem teachers who moonlighted as meth-cooks, but I was wrong on both counts. A great show transcends its genre, as both these dramas do.
If you're also doing the DVD/Blu-Ray thing and looking for stuff you might've missed, I've also got to recommend "The Wire." I know you specified newer shows and it's been off HBO for a while now, but it remains one **** of a good show if you decide to take a chance on it. It's profoundly cynical, so be forewarned--but it's also one of the best things I've ever seen on TV.
You might also like "Arrested Development," which died too young a death at the cold, uncaring hands of Fox execs. It's another show that's been gone a few years (sorry, I know I keep throwing older shows out there!), but it was an extremely clever comedy. The writers had a way of bending jokes in on themselves so that a joke in the third season had its roots in the first season. I still re-watch that show on DVD occasionally--and it's still hilarious to me.
If you're into comedies, "Modern Family" is an ongoing show that's worth a look. We first decided to take a look at it to see how it got nominated for so many Emmys; well, now we know--it got 'em because it's laugh-out-loud funny.

I generally dislike a mean-spirited comedy ("Arrested Development" is an exception to that rule, because it's pretty brutal) and I find MF refreshingly kind without ever being saccharine.