1. Tetris + Lego
Perhaps the greatest thing to come from behind the Iron Curtain, Tetris has fascinated generations. But, like the Soviet government, Tetris coldly dictates which pieces come next. Using Legos, the power could return to the people. We want to build the blocks, then drop them. Give us two pieces from which we can construct the block we need with our own hands! Control belongs to the masses, thanks to the democratic power of Legos. Does this power stem from the fact that Legos are from Denmark? Probably not; Denmark isn't known for being remarkably democratic. Denmark is mostly known for making Legos.
2. Pokemon + Nintendogs
Raising and showing off dogs is the theme of one of the top-selling games in history. But after we raise and successfully avoid forgetting to feed our dog, then what? We should be able to pit them against other people's dogs in a Pokemon Stadium-style showdown. This is the kind of vicious awesomeness one gets simply by combining two games designed for small children.
3. E.T. + Superman 64
In video games, two extreme wrongs can make a right. The Atari 2600 game based upon the blockbuster film E.T. is so bad that forcing someone to play it violates the Geneva Conventions. This is totally surprising, seeing as how most video games based on movies are solid, in-depth works of art. Just ask anyone who's played Superman 64 (and by "played," we mean "floated around and bumped into fuzzy buildings"). They'll punch you in the face, then they'll fall to the ground, sobbing and begging to be held.
One of the biggest problems with E.T. was the holes, which took forever to exit. Entire childhoods were spent trying to float out of one dang hole. This could easily be remedied by combining E.T. with Superman 64. With superpowers, E.T. could simply fly out of holes... problem solved. Plus, you don't have to worry about the fuzzy graphics which soiled Superman 64, because the flying scenes will be shown in silhouette against a full moon. These two games mesh like sodium and chlorine.
4. Super Mario Bros. 3 + Fallout 3
We've found a shocking amount of correlation between these two worlds. Massive amounts of nuclear radiation in the Mushroom (cloud?) Kingdom would explain the talking lizards, aggressive giant turtles, and radioactive flowers. Mario could wander around this wasteland, ducking into Fallout shelters whose entrances are giant green pipes. Instead of special animal suits, everyone's favorite plumber could just mutate into a flying raccoon, or a frog, or whatever.
5. Sonic the Hedgehog + NBA Jam
Sure, double somersault dunks were cool for about five days, but what if the entire level was a dunk? Sonic could receive the ball at the start of a level, then proceeds to spin and trick-dribble at 200 mph all the way through the level, hitting a giant ramp at the end and landing a backboard-smashing power slam.
Meanwhile, Dr. Robotnik and all those freaky henchmen could try to steal the ball from the blue-haired rodent by setting up trip wires and angry fans at precarious places. This would make dribblin' Sonic have to dance faster than a Japanese exchange student at Dave & Buster's.