Liberty Station on Washington Ave. Their motto is "no crap on tap."
In the Garden Oaks/Oak Forest area (north side of 610) - Petrol Station is tucked away in a little neighborhood - great tap list and good burgers. Also check out Plonk!, it's a wine/beer bar and they have really tasty wood-fired pizzas.
If you're in the Rice Village area (just a little north of where the games are and home to Rice University) go to Ginger Man, they've got a solid selection of craft brews.
A little bit further to the east and closer to downtown is the Montrose area - try Anvil, they have a good selection but a lot of hipsters go there and the service is lousy.
Avoid Flying Saucer downtown like the plague - it's tacky and half of the 100+ taps are BMC or simlar low-quality junk.