Can you give any more specifics on your tastes in boardgaming?
Dominion and Ticket to Ride are very popular games, and deservedly so, but they bore me to tears. and Munchkin.. better not to speak of that.
Questions;
how big is the table?
how much time do you have?
What complexity level of rules do you want?
etc
for 2-4 player games (that work well with 2 3 or 4), that are simples, and short i would recommend the following;
Nexus Ops: If you want a risk like war game, but shorter simpler and more fun this is it. Takes 45 mins, easy to explain, and as you win by achieving mission cards there is no ganging up. Fantasy Flight currently publish it, but the older Avalon Hill/Hasbro version is cooler. Has a neat sci fi theme.
Acquire: a game about building an economic empire and trading stocks and shares. Takes 1 hour, is pretty simple. Its a little abstract, you lay tiles and then buy shares in the hotels you think will grow. Fun if slightly cruel financial game. Not sure this works with 2 though.
Fleet; 4 player auction game about building a fishing fleet. If you like bidding in auctions and mathy sort of efficiency this is quite good. Cheap too. Despite being an auction game it works with 2.
Condottiere; A card game with a board about bluffing. You fight battles in medieval Italy by playing troop cards. Its a short simple game of double think and ruse. Cheap
Tale of Arabian Nights; This is sort of like a roleplaying game set in the 1001 Tales of the Arabian Nights. You move around the board, draw cards and have adventures from a paragraph book. Its a bit like a big choose your own adventure game. Takes a while, but you can house rule down the number of vps need to win to shorten it considerably. Its a very random game with minimal strategy.
Citadels; Another short bluffing game. Won't work that well with 2 or 3 though. You secretly select character cards with special abilities then play em and try to screw each other. Also you build buildings in your citadel for vps.
Survive Escape from Atlantis; This is the simplest recommendation i have. An island with your (and the other player) meeples on it is sinking. You have to get em onto boats and to safty. The hitch is theres loads of sea monsters trying to eat you. Great fun, I love killing all my friends most important people with sharks and watching them squirm. Takes 45mins, very very easy to teach.
Dungeonquest; This is a dungeoncrawler but the players are each on their own and racing against each other. get to the dragons room, steal monies, and get out alive be fore the sun sets. Its very deadly (Nethack or Dwarf Fortress deadly), so not for everyone. I find it very amusing.
Discworld Ankh Morpork; This is another very simple accessible game that i've taught to children and old folks. You play cards to control areas of the city with your henchmen and try to screw the other players. You have secret objectives so there is a poker element to the game.
Cyclades; If you want another light war game suggestion this game is good. Set in ancient greece with lots of cool plastic minis you have an auction for powers at the start of each turn (the power to move and raise troops, or build stuff etc). Its not to complex, quite short and looks cool.
Ghost Stories; I don't really like coop games (players against the game system rather than each other) but this is more interesting than some of the more vanilla games such as pandemic and Forbidden Desert. You are a bunch of Chinese warrior monks defending a village from hoards of ghosts. Ghost cards come up and you fight em off, sort of like a tower defense game. Pretty game components too.
If you have just two players, get Sekigahara by GMT games, possibly THE best 2 player game.