Not necessarily.. you can get zooms that cover the whole focal length range, from extreme wide-angle to extreme telephoto.
Primes tend to be smaller/lighter, with a larger maximum aperture compared to an equivalent zoom lens, and better image quality, although with regard to IQ there's really not much in it nowadays.
The 50mm (nifty fifty) is a popular option around here, as it's small, cheap (<£100 for the Canon f/1.8 version) and excellent quality.
For what it's worth, my setup (all Canon) is a 24-70mm f/2.8 L, a 70-200mm f/2.8 L, and a 50mm f/1.4. I'm planning to add a Sigma 12-24mm to that :nuts:
Shooting with prime lenses IMO makes you approach subjects differently. The fact that you can't change focal length means you have to think more about your position and camera angle, which perhaps imposes a more creative style of working. I notice the difference when I've been shooting with my 50mm.
I'd recommend you give the 50mm f/1.8 a go.. for a minumum outlay you can get into the world of prime lenses and see for yourself if you like that way of shooting and the resulting images
EDIT - one thing to be aware of, if you're not already.. you can't mount an EF-S lens on a full-frame body, but you can mount EF lenses on any Canon body, crop or full-frame. Something to bear in mind if you have any thoughts about going full-frame in the future.
A.