River City Ransom - the only Beat 'em up I ever liked.
Add stats that increase according to how often you perform certain actions,
Vehicles,
More story branches,
The ability to create your own gang and ally with others,
Hidden areas,
More, non-combat skills (Wall jump, super run, heavy lift, etc.),
The ability to enter any building,
The ability to find "special weapons" that can be drawn at any time,
Beating innocents to make the cops come after you and, eventually, the SWAT and Marines,
As few graphical changes as possible - The graphics gave a distinct taste to that game...
Give me this game and you would make me happy for many years to come.