If it's a western themed game (cowboys and such), then it's Mad Dog Mcree.
If it's gangsters, then it's Who Shot Johnny Rock.
If it's just Digitized actors (in other words not real full motion video), then it's probably Lethal Enforcers.
I can't think of any more that used real footage - try looking up American Lasergames - I think that was the company that made Mad Dog, etc.