Here's one I had years ago--probably when I first heard of Everquest:

It was an MMORPG.

It would retail in three different versions and have an ongoing storyline for one year. Anyway, there were three different MMO planets with their own plots. One was a space RPG where technology was their "magic. One was a Pokémon styled affair where it revolved around catching creatures to do your bidding. The last was more World of Warcraft, I guess.

Keep in mind that I've never played an MMORPG or a Pokémon game.

Anyway, gamers would essentially "choose their side" by choosing which game they'd buy. They'd have a full experience, too. Lots of twists and turns. After about six months, an event would occur where all three worlds came into conflict with each other. Each player would be pretty invested in their world and character so they'd try pretty hard to do their part to keep their RPG world alive.

That's the gist of it, anyway. So robots and mechs vs. giant battle monsters vs. Avatar (the cartoon).

That's my game.

And finally, there's a game that's a lot like tic-tac-toe but instead of X's vs. O's, you use Circle's vs. lowercase T's!!

Oh, I just posted that game idea to get the ball rolling. I know much of the gameplay is generic but there is some interesting ideas in there (namely the insanity effects). I feel this idea was inspired by Deus Ex, Remember Me(its combo system) and bits of Assasin's Creed. I know to actually get that developed it would need a decently sized studio. Also, I think I am terrible at naming things but, admittedly, the story behind this idea is better than most AAA games. 

Just gonna throw these out there:

Extra Credits: Mailbag #4 (1:22-1:50)

Extra Credits: How To Start Your Game Narrative

Not trying to smack you down or anything, but I think you're missing some context here.

I've recently had a really interesting thought of an original game.

You are playing a game within a game. The inner game is glitchy. The whole point of the outer game is to abuse the glitches, etc, to beat the inner game, which is actively trying to defeat you. I picture it as a 2D platformer, but it could work in almost any genre.

Now that I think about it, this is one of my worst game ideas at least according to the second video. Most of my game ideas start as interesting mechanics with the story  added on later and being ridiculous not to matter practically being a bookmark to save for later idea.

As for the first video, it is frankly just enjoyable to brainstorm some interesting idea. However, maintaining a drive to work on a game is rather difficult. I'm not even going to school for Video game design (though that is an option at my school) but, rather Electrical engineering with a possible double major with Computer Systems engineering. Game Design will probably be a hobby of mine expressing my love for the medium

is it like FEZ?

It's not impossible to make a game like that, but it is incredibly tough. It's part of the reason liscensed games tend to be so bad; they try to take mechanics from an existing story and adapt them to a game, and a lot of times it doesn't translate well.

It's great to have ideas, and try to use them, but it's easier to start with a foundation and build it up than to start from the top. Afterall, a game without a story is still a game, but a story without the game is just a script.

I was thinking of a game that's somewhat based on PS Home I guess.

Basically it's a life simulation game, but much more immersive. There's many different regions and shit, and basically depending on where you live, you'll be grouped with players playing the game that live around you. Basically you control your avatar in a living world, you start off with a house and jobless. The next door neighbors are people who live in the same area as you in real life and basically you interact with them. You have to get a virtual job to pay your bills and shit and you can lend your friends money, the game is entirely open world, you could also like, get promoted at work and save enough money to buy a plane ticket to another country, where you could visit players in france playing on another server and stuff...and even at work you interact with other players since all available jobs will be in competitive markets. So basically the game is all about being social and being the ultimate real life simulation and shit. Pretty cool imo.

I don't know for certain, having never played it, but given the description on wikipedia and the IGN review video, I don't think it's quite the same. It looks to me like Fez is about a 2D world "glitched" into 3D. I'm talking about a game that intentionally contains the sorts of glitches you would find in a bad game (or in not-so-bad games, for that matter - glitches in OoT, for instance), with the idea being that you take advantage of the glitches to progress, because the game is actively trying to stop you from progressing. Think of it kind of like Portal, in that respect - you have to go outside the "intended" game in order to defeat it.

Of course, in reality, the glitches are all entirely intentional, and tweaked to make the game work. But there would be a story-in-a-story thing going on along the way, too, as the story of the inner game would still play through, with the glitches causing you to see it in a not-so-linear way.