I'll try to stick to things you can watch on Netflix Instant and Hulu Plus and also assume you live in the US.
Animated Comedies
Archer
I'm still kicking myself for not getting into this one earlier based on really stupid reasons (I overheard a bunch of frat boys talking about it at a bar once and decided it wasn't for me), but holy crap was I ever wrong. There is a lot of subversive humor in this show and a great supporting cast of characters with Pam being my absolute favorite. This is also on Instant Netflix
Bob's Burgers
I'm a little weary of animated family comedies, but this show really does manage to find some new ground with the father being the straight-man to his ever wackier family and friends. The titular Bob is a rare treat by actually being a good father and husband in the same ways that Hank Hill was a good father, but without the same annoying redneck tendencies of Hank. The first episode was just okay, but I powered my way through the first season pretty quickly, and can't wait for season two to be added onto Netflix.
The Venture Bros.
This is probably my favorite animated adult comedy that is currently on the air right now and has been since 2006 when I started watching it. It has a really subdued style to it, focusing on an ever increasing cast of characters and their interactions with each other. There's some really twisted dark humor in this TV show and some great character and world building.
HBO Shows
The Wire
There's not much that I can say about this show that hasn't been said a hundred times before, but this really is the best show that has ever graced the airwaves. Intricate plots, amazing characters, great dialogue, and an amazing way of making you like characters who are despicable. Nobody is a saint in this show, and it does push the boundaries of your comfort, but all for a good cause. I can guarantee you that you'll be a better person after watching all 60 episodes.
Game of Thrones
If for no other reason than now you can be a part of the conversations your co-workers are having. First season did a really nice job of staying true to the book, and the second season deviated a little more than I would have liked, but was still overall quite enjoyable. There's a lot of intrigue, but it can be a little hard to follow as some characters are only ever referred to by name once, but that's what Wikipedia is for, right?
Rome
It's no I, Claudius, but it is definitely a worthy disciple. A historic drama depicting a fairly accurate look at the lifestyles of the plebs and the patricians, with a heavy focus on Caesar's conquest of the Gauls, all the way up to the defeat of Marc Antony and the formation of The Roman Empire, mostly told from the point-of-views of two soldiers who are two of the biggest badasses to ever be in the same show together. If you're a history buff, you'll get a lot out of this show, but don't feel like you need to be fluent in Roman history to understand it, it works as a periodic drama as well.
Network Dramas
Homicide: Life on the Streets
The precursor to The Wire, based on David Simon's non-fiction book Homicide: A Year on the Killing Streets which documents his exploits as he followed the Baltimore Police's Homicide Unit as they investigated the murders in a city that has between 250-300 a year. The TV show came out about 3 years after the book and in some ways is superior to The Wire because of their network censoring. While The Wire was on premium cable and could show as much blood, violence, swearing, and tits as possible, Homicide had to abide by network standards and as such had to be a lot more careful with what they could show. Now despite that, they had some incredibly heavy episodes and really did a good job at showing a different side to police detectives as colder human beings who are not phased by death, as it's a part of their everyday life. They joke about the victims at the scene and even seem to show a disinterest in the seriousness of their job, choosing instead to continue on with whatever conversation they were having on the way there. It's a show that's the absolute antithesis to the police procedural dramas of the '00's and is well worth your time. This one may be a little hard to get ahold of, but I managed to get seasons 1 and 2 for $20 at Barnes & Noble.
Supernatural
A very interesting show about two brothers who hunt supernatural creatures across the country and deal with their own personal demons and problems that arise from such a life. First season was a little too formulaic and the second was a bit too somber, but the series really hit its stride in the 3rd, 4th, and 5th. Like with The X-Files, I found the 6th season to be a little too hit-and-miss as there really didn't seem to be an overarching story, at least not until the later episodes, but I still think seasons 3-5 are some of the best network television that was on at the time. It's also on Netflix Instant.
The Walking Dead
As much of a slog as the 2nd season was, it was worth it for how good the third season has been. Unless you're absolutely sick to death of zombies, this is another show that's worth watching just so you can be a part of the conversation and get all the little memes that pop up every now and then. You'll have to endure your fair share of boring parts, but believe us when we say season 3 is some of the most compelling TV currently on right now. Currently seasons 1 and two are on Netflix Instant
British Comedies
Peep Show
A very interesting show that utilizes a point-of-view camera view gimmick with internal monologues of the two main characters who live in a kind of Odd Couple arrangement. There's some side spitting moments in this show that I really don't want to spoil, and some great dialogue between two actors who have an amazing chemistry together. It's also on Netflix Instant.
The IT Crowd
It's a British comedy that follows a more American network comedy formula with some mixed results, but overall is generally pretty funny. Despite what you think from the title, it's humor isn't based that much around technology outside of a few jokes for everyone to get, so if you're a tech head you may be left a little disappointed. Still, there's some great performances by the three leads, and a very idiosyncratic boss who steals every scene he's in. It's also on Netflix Instant.
The Mighty Boosh
Probably my favorite British comedy because of it's surreal style and focus on referential music humor. There's some real inventiveness to it, and you'll probably find yourself laughing at the bizarre nature of the show just as much as the jokes. Sadly though, this one isn't on Netflix Instant.