What platform are the games for? If its PSX or PS1 then most burners will back the games up. PS2 games you will need a DVD burner for. PC Games can be tricky, i think the best burners out there for pc games at the moment are the plextors. They seem to be able to read and write just about anything.
At the moment i have a BENQ 24x10x40, a pair of yamaha 16x10x40's, an AOPEN 48x12x50 and a Pioneer DVDR A-104. All are reliable and work aith all the common CD/DVD burning software. My personal Fav has got to be the AOPEN- burns perfect at 48x when reading from the SCSI hard drive and the just link tecxnology is a lifesaver if you forget and start MS Office up or something. The Yamaha's are solid and dependable- the 8mb of buffer is pretty good but i find they dont last all that long- after a while they just dont read CD's any more. The Pioneer is sweet. With the latest firmware you can burn a 4.7 gig disk (Around 4.3 gig of data actual space) in just over 30 mins- perfect for PS2 games
Out of the lot the AOPEN was the cheapest and performs the best- i think it cost around £45. Pretty damn cheap for a 48x burner.
I would stay away from the DVD/CDR/CDRW combo drives if i was you, they dont perform all that well. The data transfer speeds are slower than advertised and they can be querky as hell.
EDITED: My spelling again and added a bit