OK, so since she IS a computer, Portal's GLaDOS wouldn't exactly need a rig of her own. If she did, though, it'd look exactly like this.
This is the Hammerhead HMR989 from DARWINmachine. And aside from the fact it's in a rather elegant, glowing "case", its key point is that it's not really a PC case at all. Rather, it's a frame for a PC's components to be bolted to, since it's basically an inside-out computer, stuff like the drives, fan etc exposed for the world to see.
Intended for "hardcore gamers" (well, duh), the case's designer, Matthew Kim, has a "background in race car engineering", which explains why it looks like the result of a steamy night between a Formula 1 car and a Portal turret.
If you're interested, there's one available, and it costs...$2,899. Plus shipping.