This has been discussed many times here and there really is no one best drive. Nec, benq (except the dq60), newer liteon, lg, and a couple of others are all good drives, each with their strong and weak points. If I had to pick a drive that was the best overall, I would say that the latest benq's are fighting for top position, but that changes from model to model, and even changes as new firmwares for drives are developed.
Any decent burner will back up dvd's fine. As far as game backups, there are many diffrent copy protections often requiring specific software and proceedures for each. Any good drive will backup some games, but some copy protections need certain burners and as harley said, you want to look for a 2 sheep burner for that.
Look through the reviews here (there is a button at the top for them). many of the good drives have been reviewed here and the reviews usally identify which are 1 or two sheep burners (or are 0 sheep burners).