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Yes. It can. Just takes the right creative direction and willingness to change. Some examples: Mario (As mentioned), Legend of Zelda, Overblood, ect.

It can. Halo Wars was fun. But why? I couldn't imagine playing Metal Gear as a sports game.

Usually as long as it makes sense. I wouldn't want to see an Elder Scrolls Raing game, but even an RTS could be plausible. (Not good examples but you know what I mean)

Sure franchises can jump genres. I think it takes two things: the vision and drive to create in a new genre that still feels like previous titles did, and the ability to, if the product is not coming out like a continuation of your franchise, say "This is not working. We need to chunk it." The Mario and Luigi series an awesome example, I think. It's a big leap to go from a platformer to an RPG. Probably the only bigger step is to an FPS. But they pulled it off wonderfully.

Some games like Mario can be sucessfully change genres. Other games, not so much. Resident Evil anyone?

I think in the right hands it could be a big sucess. Yet now I think so many franchies are so planted in their foundation that they shouldn't. The only exceptions would probably Mairo & Little Big Planet Carting.

Halo Wars was great. I wouldn't mind if more games crossed genres. I would love a straight up FPS set in Mass Effect. Or a space fighter sim set in halo.

Resident Evil basically changed genres. It's turned into a action shooter game rather than a survival horror game.

I think for the most part it's rarely better(let alone just as good) than its original iteration. The only Shining example I could possibly think of is Resident Evil 4. Even though the game somewhat sticks to the older genre in some aspects,Overall I would consider it a different genre from the past resident evils.

It would probably depend on the franchise, the developers behind it, and how serious of a tone it has. Games like crash bandicoot and Jack & Daxter(and Mario) it seems can make that genre jump because of their cartoony style among other things.

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I don't mind games genre jumping as long as they do it right, what I do mind is a franchises jumping all over the place. I'm not a damn cash cow! I don't have the money to buy different consoles just because they decided to change it every new sequel or prequel or pre-pre-inter-sequel-spectacularthon-extravaganza or whatever the hell they're doing now. As much as I love this franchise I stopped following KH because it was to much money just to keep up with the story. How many Ansems are there now? 4? 8? 15? 16? 23? 42? 108!? i've lost count already.

It depends on the developer, and I think how much a franchise relies on specific elements of their original genre. There definitely are success stories-Mario, Metroid, etc.

Not too many games can pull it off well. Mario is an exception to a general rule of no. In general a game can't be as good in a genra crossing sequal. Games can come close but even good examples like Mario rpg and L mansion fail to live up to what started the characters beginnings. The Zelda games went from top down to 3d , but you can't call that a genra change. Someone mentioned over blood in this for the positive?? That sequal turned a mediocre if hilarious survival horror game into a hilarious unplayable adventure game. The key word there is unplayable. Actually I can think of 1 passable genra breaking game ever. Metroid prime went From side scrolling platformer shooter to a first person shooting platformer. When you think about it though the game play isn't truly a game  Changer though. More like a Mario world to Mario 64 kind of change where the core elements are mostly the same. To be a genra change much more has to Change than adding a 3 d environment. Traditionally games that try more than what metroid or Mario did fail. Mario kart mabe. I can think of nothing else that can live up to or sell near the copies of a game sticking more or less to what they have always been.

although I disagree with your premise about Chain of Memories being a genre change (it was still an action RPG at the end of the day), I do agree that franchises can successfully switch genres. I just think developers have to put in the extra work, rather than just rely on a brand name. I'm glad you mentioned Mario, because its the perfect example.

Games like Mario Kart, Paper Mario, Mario and Luigi, etc are very successful because they embrace the Mario franchise and all of its charm, and expand on it with games that have fun and addictive gameplay. Games like Mario Party and Mario & Sonic on the other hand, take advantage of the Mario name, and basically just throw the characters and locations into games that just aren't top quality.

At the end of the day, it all depends on execution. If you fully embrace what makes a franchise great and expand on it to fit a new type of genre, its usually successful.

I liked Jak X: Combat Racing.

I like them as spin offs, not a new direction.

It's possible but to me, it depends on what game and on what 2 genres.It needs to be logical and that's pretty much it.