View our recap of Minecraft Live, where the cave update and new mobs were introduced!
Quote from DragonAMiner
Make a room that's only farmland and water with a door connecting it to the rest of your house. I don't think slimes will be able to spawn on farmland, and the door will keep them out.
It's kinda hard to do slab floors if I'm underwater...
Glass floors also work to stop slimes and other mobs from spawning. Carpet over water, bottom-half slabs, fences, or stairs.