My Favorite Board Games, in order of when I see them as I look around the room right now.
Jaipur! Jaipur is a killer little two-player economic simulation. You're trying to collect sets of different Middle Eastern-themed goods, but the kicker is that you can't trade directly with your opponent. Instead, you both trade cards into and out of the market, getting rid of stuff you don't need and racing for stuff that you do need as the market is fed both from your hands of cards and from a draw deck. It has a tiny, attractive box and a frankly staggering depth of strategy for what it's made up of. Like all the best games, it takes a small set of possible decisions and lets you explore them to their absolute furthest degree.
Galaxy Trucker! Galaxy Trucker is wild. It's nuts. It's bananas. You and up to three friends are space truckers, tasked with building a ship out of salvaged parts, flying those parts around, picking up a little extra cargo along the way, and generally hoping that your ship isn't blasted apart by meteors or by comets en route. You build your ships simultaneously, putting tiles from a central pile onto a pre-shaped template, taking into account speed along with defensive and offensive capabilities, and then you go on your journey. It's a great game of goofy fun.
Quantum! Quantum is a game of tactics. You and up to three friends take control of a fleet of ships (a.k.a. dice), trying to land cubes on planets. You have to both position your dice properly and have them displaying the correct sum to land a cube. This process, however, is complicated by the fact that you and your opponents are all jockeying for the same planets, and by the fact that the number displayed by a given die determines what kind of ship it is at the moment, with each of the six ship types having a different speed, offense, defense, and special ability (all helpfully designed to match the number itself, natch).
Bonus "teach a man to fish" moment! I heard about each of these games through Shut Up And Sit Down, my personal favorite website for board game reviews.