I don't often get in the business of picking out particular purchase links, because they expire quickly and someone always has a "better deal", but ballpark your looking

Intel Core i5 3570K (the only other option on this budget would really be the i7 3770K, but you don't get much for the money) ~$220
Z77 motherboard depending on exactly which one you get (something like the Asus P8Z77-V) ~$185
8G DDR3 RAM (not really any reason to or not to get more) ~$40
600(ish)W nice power supply (something like the Rosewill RG630) ~85
ATX case (depends largely on your style) ~125
DVD-RW (no difference in these really ) ~20
240G SSD (could drop to 120 if the budget gets tight, I like the Samsgun 840 or the Crucial M4) ~190
1T data drive (no real brand preference here, just something big enough to store bulk data) $90
Video card - depending on which color you bleed. These both offer top-tier performance, with either one taking the lead depending on the game
AMD 7970 Ghz Boost ~$430
-or-
nVidia 680GTX ~$500
Operating System (Win7 or Win8 OEM) ~$100
Aftermarket CPU heatsink (just because it lets you do mild overclocks) ~$35

That comes up to around $1420-1490, depending on which video card you choose. So let's just call it $1500.

Still need peripherals:
I like a 24" IPS 16x10 monitor myself (like the Dell U2412M - $280), but most people opt for a much less expensive 16x9 1080p, which runs on average around $175.
Generic keyboard ~$25
(Gaming-specific keyboard, chunk that up to around $100)
Generic 3-button mouse ~$25
(Gaming-specific mouse, chunk that up to around $50-75)
Generic computer speakers ~$25
(Nice 2.1 setup, chunk that up to around $200)

That varies a lot, based on your preference. The computer, pretty well set in stone, it's just a matter of picking out your brand name, the basic components won't vary much from what I have listed above, and the price won't vary too much (unless you splurge for factory overclocks or exotic aftermarket options). The peripherals though, it really depends a lot on you. If you decide you want to spend more on the peripherals, there's plenty of room to drop a bit on the video card - a 7950 or GTX670 won't hurt you a lot on performance, but will save a hundred (or more) dollars on the computer portion of the budget. Cutting back a bit on the SSD (dropping from 240 to 120) saves you $80 or so. A lower model motherboard (dropping from the P8Z77-V to the P8Z77-V LE or -M, for instance) saves you around $40-$60, and you don't really lose a whole lot.