Game creation over the course of time can be a result from one of two causes: evolution or creationism. (But we're not getting into a religion versus science debate.) (Because science/evolution win of course.)
Evolution: Taking an existing game and improving upon it, in terms of graphics and/or gameplay. Examples: Mario and every other franchise.
Creationism: Every non-franchise (or the first in a franchise), non-copycat game ever made.
Here are some 'creationist' games that I've come across over time, and that I'd like to play. Despite the Mario example above, these will be strictly non-video games.
Jumbo Monopoly: Starting off with baby steps, this isn't revolutionary game design, as we're just taking an existing game and making it jumbo size, but you can't argue that this changes things completely. I have always wanted to play a jumbo sized game of Monopoly, and that desire was always fueled whenever I went to the Toys R Us in Times Square and saw that mega-sized Monopoly board on the ceiling. These kids from Columbia have apparently lived out my dream. I want to play so bad...
Riskopoly: Another step towards creationism gives us the idea of combining two games and creating one. As the name implies, Riskopoly combines two excellent games, Monopoly (normal-sized) and Risk. I have read through the rules a few times, and it seems like a great system. To very briefly summarize; you play Monopoly, and whenever you pass Go, you get to take a Risk turn. You're able to buy armies with Monopoly money at the cost of $50/army. There are lots of tweaks to the rules, but that's it in brief.
Capture the Flag with Stuff: Next is taking an existing game and just heavily modifying it. Ever since seeing this, I have wanted to play Capture the Flag with Stuff. From what I can tell, it was developed at Carnegie Mellon, and there are some pictures here. (They even had a PowerPoint presentation beforehand going over the rules!) Basically take Capture the Flag, and add in magical glyphs, wands, potions, and belts. What? Exactly. If anyone get this together, it's PLAY, so get on this ASAP.
You Have to Lock the Entry: The final evolution towards creationism (sounds strange...) is creating a new game from scratch. I came across Scott Jon Siegel when I was reading his review for Carcassonne. (Great game.) You Have to Lock the Entry is a card game he made up based on the chaotic world of Wikipedia. Very strange idea, but it looks fun. It looks like a fairly quick game where you have to move your hands quick and play fast. (Similar to speed/spit/egyptian rat screw, but not in gameplay.) Scott has a column on The Escapist (home of Zero Punctuation) called Game Design Friday, which is published on Fridays, somewhat sporadically.
Hopefully these examples inspire you to create your own games, or in the very least, play one of the games described above. Oh, and in case you didn't catch it, I'm fairly certain the title of the last game is an homage to You Have to Burn the Rope. Make sure you have your speakers on when you manage to beat it.