Board Games!

[Cheerios]

Monopoly
Chess
Scrabble
Jenga on top of a chess board
Apples to Apples
Near-impossible board games like Deadly Danger Dungeon

[Byrd]

As for board games, Diplomacy trumps 'em all for me. It's also a great way to lose friends!

Couldn't have said it better myself. Diplomacy is my favorite board game ever, by a mile. But it's way too easy for it to be so personal, people tend not to like to play it.

For hardcore board games, I also really enjoy:
18XX (particularly 1830 and 1870)
Pax Brittanica
Civilization (not the Sid Meier version)
Fury of Dracula
Arkham Horror (only played the old version, but own the new one)

For less serious games:
Settlers of Catan
Lord of the Rings (the team version which was almost impossible)
Trivial Pursuit
Dominion (not a board game, I know)

[Senji]

Smallworld
City of Thieves

Catan setup goes quick for us as everyone helps grab something, and we normally play completely random incl numbers face down.

Edit: Man, Tonko...I never seem to find people IRL that know Arkham Horror that I can learn it from. I don't like just buying a game outright without trying it first, and Arkham Horror looks pretty complicated to try to read through on your own (especially without being able to "playtest" it). I'm hoping I can get lucky at PAX East

Local game stores normally will bring/open a game to play on one of their game nights if you request.

[Norellicus]

Still the issue of finding someone experienced at it to teach me

The store(s) in my area don't host their own game nights anyway, they're all run by local paid-membership associations. Not keen on paying for a membership that I don't involve myself in 24/7.