If I could have only one gun in the whole world it would be a 12ga shotgun. From small game loads for smaller critters and upland birds, to steel shot for ducks, to slugs and/or buckshot for larger game - a 12ga can be used to hunt just about anything.
If I had to go down to a specific model, it'd probably be a Remington 870 Wingmaster. I like autos, but sometimes they can be temperamental. For a no-nonsense "It just has to work" gun I prefer a pump.
That said, I find no need to place such restrictions on myself, so my guns are pretty diversified.