Pwn or Die have come up with a good bar argument: The four faces on a hypothetical Mount Rushmore of video gaming. The four they've chosen are good, but are they the best choices?
As you can see in the pic, the selections are Master Chief, Mario, Lara Croft and Sonic the Hedgehog. Lara is the only head scratcher to me, although she does represent the 1990s PC gaming boom pretty well.
If it were my call, and we were picking analogs to the US presidents up on the actual hill, I'd go with something like:
Pac-Man as George Washington: Washington was the father of the country. Pac-Man was the progenitor of video gaming.
Gordon Freeman as Thomas Jefferson: Jefferson is on Rushmore for representing the principles of U.S. democracy. Freeman as a symbol of Half-Life 2 and Valve, likewise represents a broad set of bedrock principles for good games - good story, strong level design, memorable characters, multiplayer (on PC anyway), multi-platform, long replay value, among many others.
Master Chief as Teddy Roosevelt: Roosevelt, the progressive, also is the most recent of the four faces. So is Master Chief, whose game likewise represents progress into a new era of gaming.
Mario as Abraham Lincoln: Lincoln saved the Republic. Mario, through Super Mario Bros. and the Nintendo Entertainment System, saved console gaming.
I agree Gordon may not be an iconic choice to non-gamers; maybe less so than Lara. But hey, it's not like this actually exists somewhere. So who would you put up on yours?