None of these are two player, sorry, but here are some of my favorites:
Settlers of Catan. Yeah, it's practically mainstream by now but still worth mentioning. It's well-known for a reason: it's a seriously good game.
Catan is a lot of fun, easy to learn, and pretty easy to set up.
A few others I like areZombies
: Fun, campy Zombie-themed board game where the players are survivors trying to get to the helipad and killing lots of zombies, or getting killed by zombies, on the way. The board is built out of square cards that are added as the game continues along, so you'll have a different board (theoretically) each time.Betrayal at House on the Hill
: OMG is this game fun. Super easy to learn, quick to play, and has an even campier feel to it than Zombies! You build the board out of cards like in Zombies, but the game takes the randomization on step further by making one or more players the betrayer. Basically, there are two three rule books: one for general game play, a scenario book for normal players, and one for the traitor(s). Everyone chooses on one of the pre-generated characters with basic stats, and they explore the house. After a certain point, the traitor is revealed, and the game proceeds down one of 50 or so random scenarios based on classic horror tropes. The player(s) who is(are) the traitor(s) get the traitor rulebook and find the scenario and learn their objective, while the normal players get their scenario rulebook and learn their objective. The two sides then compete. One of the best board games I've ever played. One warning though, the recent release of the game has most of its parts made out of really shitty cardboard, and they will warp easy. Not unplayable, but the pieces won't lie flat. Not a two-player game unfortunately.Arkham Horror
: This game is fucking crazy. It took me and my friends 6 hours to play through this game our first time through. It has a ton of rules, and is not easy to learn, but it is FUN. It's cooperative, as in you and the other players are investigators who need to stop one of the Old Ones from the Cthulhu Mythos from awakening and fucking shit up. You all win or lose together (most of the time). You fight monsters, explore a large map, collect items and seal otherwordly gates. It's almost like an extremely simplified Pen and Paper game. You can play it solo or up to like 6 players. Not an easy game, both times I played we barely succeeded, which makes things very exciting.
Outside of Betrayal, these games can be played two player, but are best with a group of 4 or more. But not having such a group doesn't make them not fun.