I've had good experiences at this copy center. I've bought many course packs for my classes at the UW here, and I trusted Rams to bind the portfolio I needed to apply to graduate school (which they did right on the spot). Their prices are fair and the binding work they did for my portfolio was above my expectations. Try to avoid the store during the first week of the academic quarter as students swarm to pick up course packs...
Best desktop publishing in the U-district. Why pay exorbitant rates at Kinko's when just two blocks away, there's a friendly, far more economical place to go. I have rented computers here, purchased business cards and bulk printing all for a 1/3 to one half what Kinko's would charge. I love this place.
PROS: Economical desktop publishing
CONS: Not open late
For general photocopies I tend to like Ave Copy a little better which is practically across the street from here - there's no shortage of copy shops on this stretch of University Way. but I think Rams Copy Center might be a little better if you're coming to use their computers and make a print out, or something like that.