Dumprep.exe is a Microsoft process that runs when a program has a critical error and cannot be restored. Basically it comes with XP/PRO. It's a non-essential program but I'm not sure how to stop it from running. I would search microsoft.com until you find information on it or a simple google.com search might yield better results.
It's not a virus or anything although spyware can assume the same name as this Microsoft software (as with any process, spy ware can "mask" itself as a legitimate OS software). You can run Search and Destroy, CW Shredder, Hijack This and a slew of other free utilities to get rid of spy ware on your system if you suspect you have it. Hijack This is the best tool (do a search in google and it will come up) HOWEVER it is a very complicated program and should only be used with extreme caution. I'll say this once, LOOK UP EVERYTHING that Hijack This brings up on your system with a google or Yahoo search before clicking remove as it brings up essential programs that you need to run your system as well as spyware threats.
Okay, that being said, a better description of dumprep.exe that you would recognize are those annoying messages that ask you to send data to Microsoft when a program crashes. It either asks you to ignore the error or send data to Microsoft. I always choose to ignore the message instead of sending it to Microsoft. One, because I'm paranoid and I don't want Microsoft to know what programs I'm running (not because there is anything top secret on my system, I just don't like big business knowing my business) and secondly because when you send the data to microsoft it builds a file that is stored on your system. Eventually the file becomes very large and you have to go through all this hooha to delete. It's just annoying.
I wouldn't worry about the dumprep.exe process too much but you should run spyware blockers and at least run Search & Destroy on your system just to eliminate the possibility of spyware.