From my experience, it depends on the game and what kind of "ripping" you want to do. For example, do you want to capture in-game footage, or do you want to use the cutscenes (assuming the game has cutscenes)?
If you want to do the former, there are programs out there that allow you to capture whatever happens on your screen; unfortunately the good ones aren't free. Check out programs like
Camtasia or
Fraps (both of which have free trial downloads) and see if those don't get the job done.
If you're going for the cutscenes, you might be able to simply pull those from the disc, although this isn't always as straightforward as it sounds. For example, when I wanted to take the cutscenes from my PC version of FFVII, it was really easy - they were just on the discs and I simply had to copy them to my computer. However, the videos were in a different format for my PC version of FFVIII, and I had to do convert the files to a readable format.
It all depends on the game, at least from my experience.
And for the record, American McGee's Alice isn't considered anime, if you were planning on using it solely in an AMV project, so your video probably couldn't be hosted here.
