You don't NEED a GeForce 6xx series just to play the games you want. You could get a 5xx series, or even a 4xx series and play those games on very nice settings if you wanted. The thing is that your ENTIRE SYSTEM brings games to life, it's not just all down to the graphics card. The GPU is a large part of it, but it's not everything. That's why people are saying maybe you need a new system because that other stuff matters almost as much as the new card. The CPU, the amount of RAM you have, how FAST the RAM is, your hard drive's spin speed... lots of little things affect how well your system handles games. Everything matters.
And don't you dare forget the other most important thing when you're upgrading to a new card. You may need a new power supply!!! Even though we live in a much more advanced era of technology than say... 5 or 6 years ago, it's likely that you may not have enough power to RUN a new card if you try to install a new one, and you might even destroy your system if you installed one without the right power supply. It depends on if you built your system yourself or not. If it was a store-bought computer, you might not have enough power, or the supply may be of low quality.
If you're going to run a modestly powerful system, I suggest a minimum of 650 watts of power to run everything you need. Make sure to pick one from Thermaltake, Corsair, Antec, or maybe Cooler Master. Any other brand and you might be getting an iffy power supply. But a good 650 watt supply with an 80%+ efficiency certification should more than easily cover you unless you start running multiple graphics cards... but nevermind that. 650 watts minimum, and anything from a GeForce 460/480 GTX all the way up to their 6xx series cards should easily do the job. And if you want to try AMD's side of things, anything from their 6xxx series to their 7xxx series should do, but will recommend that you stick with the 6870 and above for serious gaming.
Here's a good tip with Nvidia cards: If you want a nice card from Nvidia, always make sure you go for a model that has GTX or Ti in the name. GTX and Ti are always given to their strongest cards of any series of cards they design. If you see names like GTS, GTO, or even GT, I'd stay away. The GT cards aren't too bad, but if you're a performance nut, they don't quite have enough punch.
If you go for a card from AMD, make sure that the last two numbers are 70. Examples: 7970, or 6870, 7770, 7870... Any of the ones that have 70 at the end are the much more powerful cards.
One more good tip: check how much memory the card has built onto it. The models with more RAM are the better ones. So if you see something like GTX 660 Ti 2GB, go for that over a 1GB model. You will see better performance. The same goes for any card from any manufacturer. More memory is better. The problem is that the models with more RAM cost a lot more.
These tips are a little simplified, but will definitely steer you in the right direction. I don't want to get too technical and give you an info overload. If you have any questions at all, post away. There is no such thing as a stupid question. I'm sure we'd all happily teach you.
I will also very happily post you the specifications for a system for around 1000 bucks if you want and you can order the parts and build it yourself.
