Inspired by the Mythbusters zombie thread, I think this question is pertinent. I think the Friends cast is one example, and NPH is friends with Alyson Hannigan, but what else.
I know Zachary Levi and Joshua Gomez are great friends on the set of Chuck, but I don’t know if that extends to their private lives.
Vaudevillans Smith and Dale were very close and are buried in the same plot along with Dale’s wife Molly (Smith never married).
Though they haven’t really worked together in years, I think we can count Hugh Laurie and Stephen Fry, who are genuinely close friends in real life and have been since their university days. Fry was the best man at Laurie’s wedding and is godfather to at least Laurie’s eldest child.
From what I’ve read over the years, the large regular cast of The Sopranos were, and by all accounts still are, pretty tightly knit.
I hate that I know this, but Anne Hathaway and Emily Blunt from The Devil Wears Prada are bestest pals.
Onscreen brothers Sam and Dean Winchester of Supernatural are portrayed by Jared Padelecki and Jensen Ackles, who are good friends offscreen.
The cast of Firefly are pretty tight. Or at least some of them are. Nathan, Alan, Jewel, and Morena are always twittering about each other, and hang together whenever they can, which is admittedly rarer these days.
From what I’ve read, Matt Smith and Karen Gillian (The Doctor and Amy Pond) are pretty good friends off screen and hang out quite a lot.
Just based on Twitter, Allison Brie, Danny Pudi and and Donald Glover seem to spend a bit of downtime with each other outside of filming Community.
Zach Braff and Donald Faison roomed together during the first and second season of Scrubs.
I used to work at a theater where they were performing Love Letters - a two person cast (one male, one female) and they would only perform one week and then the next two person cast would do the show. These were always with big name actors and actresses and the show ran for over two years - so we had lots and lots of big names.
In regards to your question, there were literally hundreds of celebrities who would come to see the shows, and then wait and go back stage to meet with the celebrities who were performing in the show. If this is any indication, it seemed like there were lots of friends in the acting community who would make the special effort to come see the show and get together afterwards for at least dinner and drinks. It was very rare for performers on stage NOT to have some celebrity out in the audience cheering them on and rushing back stage afterwards.
Grace Park and Tahmoh Penikett (Sharon/Athena and Helo) on Battlestar Galactica were good friends offscreen – IIRC, they even shared a house (along with Park’s husband, but…not like that :)) during the final season of filming. Penikett was also good friends with Katie Sackhoff.
Judging from the rapport on the DVD commentaries, the Arrested Development cast seemed to get along swimmingly.
Not a TV show, but movies, Simon Pegg and Nick Frost are best friends and were before getting into the movie business. (Their work includes Shaun of the Dead, Hot Fuzz, Paul)
A more famous Hollywood example would be Kevin Smith and Jason Mewes.
The “kids” on Glee are supposed to be quite close and go out together even when they’re not working. I hope for their sake that it’s true they all get along well, as they must spend more time together than most television casts – the past two summers they were all performing in the Glee concert tour.
Who were also best friends long before their entry in the movie business.
Expanding this out to the entire Askewniverse, Smith is also good friends with Jason Lee, Ben Affleck, Eliza Dushku, Alanis Morisette, and Seth Rogen.