Well I have many favorites and the only ones that make sense would be Halo and Gears of War, Resident Evil and Gears of War, and Mario and Sonic.
Halo and Gears could easily be a crossover that has no canon to either series just one huge what if that takes place right after Halo 3 and between Gears of War 2 and 3. So it's like Sera could be the planet that Master Chief was nearing at the end of Halo 3 that takes place in the 18 month gap in Gears 2 and 3. So Chief lands on Sera and eventually teams up with Delta Squad. The Covenant will also invade Sera and try to destroy it(as if the Locust weren't already doing a good job of that). I would also like it to be all in third person. So what if Halo is an FPS? It could work just fine. It would be so kick a** seeing Master Chief holding a Lancer being face to face with Marcus Fenix. That, and I've always wanted to chainsaw an Elite.
Mario and Sonic would be so awesome, I can already imagine what it'll look like. Something happens in Sonic's and Mario's world that causes them to leave their own dimensions and into each others. Sonic goes through levels collecting stars in environments you'd usually see Mario in with the help of Mario's allies and Mario goes through environments you'd usually see Sonic in collecting Chaos Emeralds with the help of Sonic's allies. It could all lead up to an epic boss fight that features both Bowser and Eggman.
As for Resident Evil and Gears...The story would need lots of work but they do kinda work together. Both action games, third person, and bloody. It would be an epic action game. They could probably make it scary if they want to stay true to Resident Evil because the first Gears did have a very cool dark atmosphere. It was also creepy and maybe even scary to an extent. So yeah, it could work if they kept it like the first one with Resident Evil characters, zombies, puzzles, splitting up, teamwork, etc.
These are all great series and I think they can work really well together.