So you want to make a cross stitch of a video game character do you? Dating/Married to a gamer? Or are you a gamer yourself? But wait - where do these people get their patterns? Is there a website?
Actually there are a LOT of websites. Look up 'video game sprites' on Google and you get hundreds of thousands of results. (As of today I got over half a million results - and that was just websites not sprites.) The key then is to find the good websites out there. No website has all the sprites you might want, so Google searches and the like are your friend. But it is nice to have a place to start from.
Here are a few websites that can start you on your spriting journey.
The Spriters Resource - An excellent website with lots of games. This resource seems to be the site that collections go to when other sprite sites give up the ghost, plus they update regularly.
The Video Game Museum - They have some wonderful screen shots. An excellent place for opening shots - for those of you who like stitching the giant projects. Plus they have a lot of systems to choose from.
Video Game Sprites - Over 30,000 sprites, plenty of game systems to choose from.
Deviant Art - This site is a treasure trove of custom sprites as well as ripped ones.
Just a word of caution though in using sprites. For the most part, you will not own the copyright to characters (even original custom sprites). Selling the crafts you make with the sprites can get you in trouble. It's better to not chance it. However, if you post your stuff in a gallery format, you should be fine.