The answer is yes, you will be able to install Starcraft II on any future box you have.
Soon after you purchase Starcraft II, you will link your key to your battle.net account. If you don't have a battle.net account yet, you will have to create one. You must link your key to play the game.
Once your account is linked, you never need your key again. What's more, you don't even need the install disc again, as you can download the entire game client off the battle.net site. The disc itself is just a convenient way to install the game; I myself bought it and didn't even use it. The same is now true for any PC Blizzard game released in the past 12 years, including Diablo 2 and the original Starcraft.
What's more, for Starcraft II your match history, achievements, and current campaign progress will also transfer because it's stored on the server. There may be some stuff like Replays which won't transfer over to your new box, but for the most part you will be playing the game where you left off.
The only way you could hose yourself here is by somehow losing access to your battle.net account, for example by forgetting your password or permanently losing your internet connection. I'd recommend against that.