Will the activation key let me play on multiple computers?

[River]

I just bought the base game and some dlc, and I wanted to install them on my laptop for now, and then when we get our new desktop computer in a few weeks, I want to install the game on there and throw this hunk 'o junk out the window. BUT I don't want to use my included activation keys on my laptop if that means I will ONLY be able to play on my laptop.
I know Steam is generally pretty cool about allowing any games on an account to be played from any computer as long as you're logged in, but I also know EA is a jerk who doesn't play well with others. So. If I activate the keys now, am I screwed in the future?

[Ventorian]

You can resownload all your steam games onto another computer, however unless you transfer all the steam files from one computer to the next, you will lose all local content, like saves and such.

[cruinne]

Actually, it's not the Steam files you need to transfer to keep your saves and custom content -- it's the "The Sims 3" folder inside your computer's Documents directory. That's where all your games, content, saves, and such are stored.