I posted this in reply to SS2Dante:

Any time two genres or niches are combined, there is a tension there that gives the potential for a hybrid that is more than the sum of the parts. Certain elements of each battle the other, and it can be difficult and painful, but in the end, the results can be good.

We see this all the time in modern music, where country and blues gave birth to rock, something distinctly different than either parent. Lately, the trends have been a combining of rock and techno (to mixed results of good and bad) and rock and hip hop (to also mixed but occassionally sublime results), in my humble opinion.

Creating a hybrid can be very risky. In fact, it often produces monsters, hideous mutations with the strength of neither parent. Take, for example, the time Homer Simpson tried to breed the dog and cat. "Soon I will have the perfect hybrid. The loyalty of a cat with the cleanliness of a dog!" But when it's the other way around, it can be very cool indeed. Some of the most successful hybrids are now established and common subgenres of their own.

Consider:

Strategy/RPG:
The character depth/development/specialization and plot of an RPG with a battle system that's more involved than mashing the "attack" button over and over on random encounters.

Action/Stealth:
Life's more fun when you have options. Instead of forcing you to take one path and gameplay style, you can mix it up. Consider MGS, Deus Ex, Mercenaries, etc.

Action/Adventure:
It may be common, but it's still a hybrid. An adventure game can be more than trying to find the right item to solve the puzzle. It can be combat and platforming too.

A few hybrids I'd love to see someday:

RPG/2d or 3d shooter: Customization options and depth of an RPG, but with furious shooting action like old-school (or new school) shooters. The closest I've seen is in mech shooters like the Armored Core series.

Stealth/Strategy/RPG: It looks like MGS Ac!d may already fill this void, but I haven't played it yet. Plus I'd like to see one without needing cards.

Vehicle/Platformer: Perhaps the closest are games like TrackMania or Diddy Kong Racing, but I see a lot of untapped potential here.

Multiplayer Shooter (1st or 3rd person)/RPG: Action-packed team or DM with different classes of characters and roles to play. A bit like Heretic or Rune with healers and summoners or an MMORPG with real-time battles (not slash/hack with damage/second).

Pokemon/Platformer: I realize that Pokemon is already a hybrid variety of RPG, but consider if you had a game that played a bit like Mario 64 but with the monster collecting of Pokemon. You could have your monsters fight for you in real time, give them commands, ride on some of them to get to certain places, etc. I think it would be a must-have game, but I'm surprised Nintendo hasn't even tried it yet.

I've already mentioned a few games that could be close to these hybrids I've thought of, but if anyone can think of more great hybrids or existing games I might enjoy because they fill one of these and I may not know of them, then please post away!