Recently graduated from Abertay's BSc(Hons) Computer Games Technology and currently working as a games programmer for a small firm. Several of my peers are now working at some of the big games companies (Some are members of this forum so I'll leave it up to them if they want to share their employers names).
The course covered both console (we worked on Yarozes however the modules are now for PS2)and PC coding (C, C++, Java, OpenGL & DirectX) aswell as covering stupidly difficult maths and physics as well as more standard computer science stuff.
By doing a games related degree you cover alot stuff to do with graphics programming and simulations that I don't think normal Computer Science courses will cover.
Of course it depends on the degree, Abertay's Games Tech course is very difficult and will demand most of your life in the latter years but it will give you the skills and knowledge to build games. Personally I'm not sure of the value of some of the "Games Designer" courses that have popped up (no offence to anybody who is on one). I like so many other people want to be a games designer but I don't believe any serious company will employ you initially as one, IMO the only way to get there and be good at design is to do the grunt work and really get an understanding of how a games is produced.
One thing you have to get used to if your on a video games related course is explaining to people that you don't actually have any actual classes in "playing games" and that can get really annoying after you've been up all night coding.