There was a time when video games meant you controlled one moving colored object and you interacted with other moving colored objects.
Actually, that's still the definition of video games. But as time has gone on, the ways in which you interact have changed. In ye olden days, you either shot at or jumped over everything, or maybe if the game was daring you hit it with a sword. Here are some concepts that you'd never think a great game would come out of, but they did anyway.
1. Wild Arms
Wild Arms is, at it's barest of bones, a turn based RPG. That's not really that unusual, but the setting is. RPGS most of the time are fantasy affairs with the occasional sci-fi or dystopian based games. But Wild Arms is a western. Guns, Cowboys and Biff Tannen doing headers into shit. That kind of western. The game took a while to catch on, as it wasn't until Wild Arms 3 that people really started to get some attention, but the original is a cult classic that is worth a look for the bizarre concept alone.
2. Sonic the Hedgehog
We're all so very familiar with Sonic at this point that it takes a bit to think about how odd the concept is. In a game based on speed, why choose a hedgehog? They're not exactly known for quickness...why not a rabbit or cheetah or some shit? That being said, Sonic turned out great (though he has since sucked hard), but this is despite being a hedgehog, not because of it. There are also several iterations of the character, but the original is really strange, as it puts him as an alien from a faraway planet fighting against a guy named "Robotnik" who makes robots (what are the odds?) though he's now more usually referred to as "Eggman" because he looks like an egg (once again, wtf). The games got even weirder, what with his mutant sidekicks and whatnot, but the original was based on a foundation of weird shit.
3. Katamari Demancy
System: PlayStation 2
You know they had to be smoking weed when they came up with this idea. It's a game that uses the bare basics of controls, you only use the PlayStation 2's two joysticks and roll around a sticky ball. You roll over shit smaller than you and it sticks to you, making your ball larger. Having large balls is the name of the game, and simplicity is the other name of the game. It's shockingly addictive and fun despite it's primitive graphics, weird design and oddball characters.
4. Fat Princess
System: PlayStation Network
Fat Princess is a capture the flag style war game, the idea of these sorts of games is to command units to get into the oppositions area, get their "flag" and bring it back, at which point you win. You also have to protect your own flag. In Fat Princess, the flag is actually a petite little princess, and aside from your little alien homonid looking fuckers going around murdering each other, you'll have to protect your flag. You protect your princess by force feeding the bitch cake until she bloats up like Rosie O'Donnell. This makes it more difficult for your opponents to bring her back quickly, and it will require more of them to pick her up (kind of referencing another game you'll see on this list...) The game is simple and fun with a hilarious concept, and if the PlayStation 3 was worth it, this would be a good choice.
System: XBox Live Arcade, PlayStation Network, PC
Ah, Braid. Braid is a really great game that at first seems like a basic old-school style run and jump platform with a lot of puzzles to solve. Even the game's usage of "rewinding" time to undo things, including your own death, is really not all that unusual (I see it as an evolution of some of the concepts that came around in Viewtiful Joe), but the story is a weird ass concept. You play as this little Angus Young looking guy trying to rescue a princess, only to find at the end that you're somehow the bad guy. Some people have suggested that Braid's storyline isn't even about saving a princess or being a stalker, but an allegory for nuclear holocaust. What is really strange is the game is already great without being deep, it could have been a standard you save the princess she blows you type thing. But they went that extra mile to make it weird, and the game was better for it.
6. Plants vs Zombies
System: PC, XBox Live Arcade
Well, most of Popcap's games are strange concepts like rearranging gems and whatnot but this really takes the cake. I had heard the name "Plants vs Zombies" and the title alone made me want to check it out, and after getting a very spirited reccomentdation from a co-worker I had to try it. Basically it's a tower defense game, but your towers are plants and the "creeps" are zombies. The game is challenging, simple, quirky, funny and there's a lot of meat there with 50 levels and loads of mini games, puzzle games and other shit to play. I am hopelessly addicted to this game, the one where plants fight zombies.
7. WarioWare Inc. Mega MicroGame$
System: Game Boy Advance
Oh man this one is W.E.I.R.D. In WarioWare, Wario decides he can make a load of money making video games, but all of his games last about 5 seconds. These "microgames" are great, as you get a single word command telling you what to do and you have about 5 seconds to figure it out. Most of the microgames are really simple, but some take a few tries to even figure out. There's also a lot of them based on classic Nintendo titles like Zelda or Punch Out. The game spawned many sequels, and they continue to get weirder and better.
Oh man. I fucking love this game. Pikmin is the game where you play as a tiny little space captain about an inch high who crash lands on an alien planet (Earth) and has to repair his ship with the help of little grass-like creatures called Pikmin. The game is simply amazing and defies description, you simply have to try it out to understand how great it is. The colorful and happy tone belies the game's plot, where Olimar gets increasingly despondent as the game's 30 days wear on, as he'll die from Oxygen poisoning if his ship is not repaired on time. The game launched an even more amazing sequel, Pikmin 2 as well as Wii re-releases and a soon to be third entry into the series.
9. Shadow of the Colossus
System: PlayStation 2
You gotta hand it to Team Ico for making Video Games into an art form. Their first effort, Ico was already amazing, but it's not really that weird, standard save the princess/love story action/platformer/puzzler. It's prequel however is strange and wonderful. You are once again attempting to rescue a lady, only this time she's asleep and you have to beat several powerful bosses to break the spell and awaken her. Now that's not all that strange, as it's basically the plot of Zelda II. But what's strange s that there are no enemies in the game, only the bosses. And there are no levels either. You simply travel to where they are and beat them. The game is blissful and basically fun in a box but a concept where a game is nothing more than a few boss battles? Amazing that they pulled it off.
10. Wario Land II
System: Game Boy, Game Boy Color
Wario makes his second appearance on my list. This is the game that transformed him from a Mario stand in to a verifiable gaming star. There were already two games previously, Wario Land: Super Mario Land 3 and Virtual Boy Wario Land but they were standard fares where you ran jumped and shoulder charged your way through levels, finding treasures and coins and using special hats to power up. However Wario Land II did something amazing and did something different. You can't die. Ever. The game's entire concept is based around the fact that Wario can't die. Get hit by an enemy? You get knocked back and lose some coins. Fall down a ravine? There's a whole area down there to explore. Wario even had to get hit at certain points, as certain types of damage would change him. Get stung by a bee and he swells up and starts floating upwards. Get burned and he can run around while on fire and break certain blocks. Get flattened and go through small areas. Concepts such as challenge in a platform game were challenged themselves and even the idea of boss battles had to be re-thought. The game got a sequel, Wario Land 3, which follows the same tone. Wario Land 4 and subsequent games would give Wario a life meter, and they were also great. But it all really started here with a really strange concept.