Time to upgrade CPU?

Yes to a new motherboard that uses ddr3 ram. Intel has both socket 1155 and 2011 boards. Your performance improvement will depend alot of what you use your system for. I would list your old specs and what you use your system for for better advice.
A firm budget would also help.

You would need a new mobo, furthermore i'd recommend waiting for haswell unless you really want a new computer.

I'm not sure about all my specs, but here's what I know...
CPU: Intel Core2 Extreme X9650
Motherboard: No idea
GPU: Nvidia GTX 480
Memory: Corsair 2x4
PSU: Corsair 850 watt

I only use my system for browsing around youtube and playing games, such as BF3, PS2 (when it's not laggy), Skyrim, Crysis, etc...

If you think you need to upgrade then upgrade. You will need to change the mobo and RAM to upgrade to Intel's Ivy Bridge... or AMD if you decide to switch.

As mentioned above, Haswell is going to be released this summer. It is socket 1150 so it is not compatible with motherboards designed for Sandy Bridge / Ivy Bridge. The increase in performance is unknown so far. I'm guessing 5% - 10% above Ivy Bridge (at the same clockspeed) since Intel is focusing more on lowering power consumption than increasing performance.

AMD is also expected to be releasing the Radeon HD 8xxx series if you have no preference for GPU brand.

Generally speaking, most games are limited by the GPU rather than the CPU. So if you plan on upgrading the GPU as well, you may want to do that 1st before upgrading the CPU. That way you can upgrade the CPU later.

I don't care what GPU brand I have, whatever works. I really don't need a new computer for now because I can run all the games I play without any problems, but I do plan to upgrade sometime. But I was wondering if my CPU was lacking in terms of power for the newer games.