Yes, you can have your SSD exclusively have the OS. In my setup, I also have all my primary applications installed on it as well. Games and other applications I leave off on another hard drive.
The problem you're describing though is that one of the system folders in Windows is the Users folder. This is where all of the user-specific program configurations and temp files get stored. And over time this can grow quite a bit, considering that also, most programs don't clear out what they left there. If you want to move the Users folder: http://lifehacker.com/5467758/move-the- ... -windows-7
(this works best if you just installed Windows).