EA's Origin service is now offering the original Dead Space as a free download with no strings attached beyond requiring an Origin registration. They explain on a new page devoted to a new "On The House" promotion:

Free?! What's the catch?
There's no catch. Grab full games, expansions and more at absolutely no cost. Just make sure to act fast because On the House specials can appear and disappear at any time.

You mean a trial or demo, right?
Nope. You’re getting a full version of the real game — for free!

How long will I own the game?
Once you’ve claimed your game, it’s yours to keep!

Why is Origin doing this?
We're gamers, too. We appreciate you making Origin your gaming home ... and besides, who doesn't like free stuff?