Great games, like great bands, often combine a range of influences to arrive at their own unique style. Mashup artists, in contrast, usually combine two already popular songs to create unexpected and interesting new sounds. What would a game design mashup look like? Here are some short mashup concepts, but I invite you to post your own in the comments box. (or name games that qualify as mashups)
Centipeggle - a combination of classic arcade game Centipede and the fantastically addictive Peggle (which itself borrows from pinball and pachinko). Instead of mushrooms, there are pegs. The enemies which move down the screen are also made of pegs and shooting the ball at them removes them in the standard Peggle fashion (note that this means gravity actually works upside down with the ball falling towards the top of the screen).
Tony Hawk's Tomb Skater - Tomb Raider and Tony Hawk both share an emphasis on exploration and movement. They also both include deadly spike pits. And what could be more fun then grinding, olleying, and kickflipping your way through ancient temples to grab priceless artifacts of ancient cultures? (rather than the letters S-K-A-T-E) You get the satisfaction of both robbing the dead and destroying ancient architecture by wearing it away with your trucks. Unlocking new areas by performing certain tasks is another shared design element. And the special system of Tony Hawk grants you increased speed as you perform more ridiculous gravity-defying combos, which would be a great way to create difficult platforming sections. Slap a faster drain timer on the special bar to force the player to pull off a lot of quick combos to get up enough speed and then make them grind, flip, and spin their way through traps and over pits to the next area. There's also nothing more satisfying then wacking enemies with your skateboard or running them over on your way to the next vert ramp you have to launch off of to grab that ruby the statue is holding.