I'm running a Core i5 3570 and can run most games on Very High at 1920x1080 using a Radeon 7870.
Actually similar to Mindovermaster's rig.
I've tried overclocking in the past and it USED to help out in certain circumstances, but I typically don't bother anymore. I've been very happy with the performance on mine. I just built it about a little over a year ago. The only thing I want now is a 1TB SSD for my games. I put OS and most other programs on my 120GB Samesung 840 Pro, then games on the spinning drive. My Steam folder is about 900GB or so.
You'd be better off putting your money into a decent video card, than an i7. You could pretty easily get into an i7 and decent card, though if you don't have a huge need for storage and cut down on RAM, etc. 8GB is a good number to be at. Skimp a little on case, etc..
Here is a cheaper build as well. (Note: I would definitely spend more than these, but goes to show you that you can play current goes on a budget.)
There are a ton of others if you look up "budget gaming build" or "mid-range".