Shuttle mission STS-51 suffered an engine failure but still completed successfully (although at a lower than intended orbit):

http://en.wikipedia.org/wiki/STS-51-F

STS-93 also shut down an engine (although not as dramatically):

http://en.wikipedia.org/wiki/STS-93

The answer is really: yes, minor issues happen all the time. Something as dramatic as an engine shutdown (as in CRS-1) is rare but not unheard of.

With Falcon9/Dragon -- none of these issue have resulted in failure to reach orbit or complete main objectives. If SpaceX weren't under such close scrutiny, we probably wouldn't notice the issues Dragon had on this mission.