Brakes - they sieze up pretty bad. That's why I first went brakeless - tried to use my front brake and it just stuck shut.
Chains if they're not stainless.
Last year I had the bolt that you use to adjust forward/back up/down on your seat get filled with salt, to the point it was basically welded in place, and the seat loosened and wouldn't stay in place. That sucked.
If you have the option, keeping the bike outside or somewhere below freezing is actually the best. The salt only really gets into stuff when the snow melts. And don't put the bike in your bathtub - your landlords will hate you, because it clogs up the drains really quick.
Someday I'll invent an indoor bike-drippings stand to keep your bike from making huge puddles. As it is now, I just use an old blanket...