So I see a lot of game specs have under the video card section phrases like "NVIDIA GeForce 7600 256MB or ATI Radeon X1650 256MB or greater". My question is, what is 'greater'? And how do you tell at a glance? Or do you pretty much have to follow tech news closely to know that?

For instance, the sticker on my laptop says that my graphics card is GeForce 310M 1GB. Is that considered 'greater' than the GeForce 7600?

No clue. This is why I have an Xbox. Problem solved.

It's pretty much something you have to follow, and the numbers can get a little confusing and it gets even worse when you try to desktop graphics cards to mobile graphics cards. A good place to start would be http://www.tomshardware.com/charts/graphics-cards,1.html, although if you're comparing mobile to desktop graphics I usually just google the mobile card and find a page that gives a comparison.

Basically, it requires a certain amount of dedicated memory. Said memory is actually a part of the graphics card.

Then is it safe to say as a rule that, if the minimum graphics card is 256MB, my 1GB card will do fine?

That's a bummer. If I didn't know better I'd say that they made it confusing on purpose. The graphics chart seems to be sorted by year, which I'm not sure is helpful, since I have no idea what year my card is from, and what year the stated minimum card is from.

Is it possible to rank all graphics cards (at least, by the same company) incrementally, and if so, is there such a list?

I vaguely remember seeing a site where you can enter a game and the site will calculate if your specs are up to minimum or optimum standard for that game. Anyone know what I'm talking about, and if so, do you remember the name?