Seriously would recommend an AMD FX 8350. You will save money (even over an i5) and for gaming it packs more than enough punch (8 3.5GHz cores ). Contrary to what someone said above, it doesn't require water cooling. You shouldn't be using the stock cooler with an Intel or AMD though in a gaming machine, so look into something like the Coolermaster EVO 212 (about 30$ give or take). Also if you like it overclocks nicely to 4GHz and higher (obviously requiring a better cooling solution the more insane you get). The only deciding factor after that will be which GPU you choose. Paired with 8GB RAM (16GB is nice too but not essential) and a nice video card (nVidia 770 or AMD 280x are good value for $ cards), you should be able to run anything on high settings.
Intel's a great but there is also a massive hype, and a much larger price tag associated with that hype. That said I have an i7 4700mq in my laptop and love it