Alright, here goes.
CPU - Intel Core i7-3820 Sandy Bridge-E 3.6GHz (3.8GHz Turbo Boost) LGA 2011 130W Desktop Processor BX80619i73820
http://www.newegg.com/Product/Product.aspx?Item=N82E16819115229
Price: 309.99
Should be a VERY future proof CPU unless some major technological development happens over the next year, which is unlikely. Believe it or not, the other guy picked you out an APU, which means you have the graphics integrated into the CPU. Not a very good option for gaming, and it really hikes up the price of the CPU.
GPU - MSI Gaming N770 TF 4GD5/OC GeForce GTX 770 4GB 256-bit GDDR5 PCI Express 3.0 HDCP Ready SLI Support Video Card
http://www.newegg.com/Product/Product.aspx?Item=N82E16814127747
Price: 399.99
Had to somewhat skimp out here, since the price difference between this and a GTX 780 can be $100+. In reality, though, it's not really skimping out because the performance change between the two isn't significant enough for a person to notice. It should be able to run games like Battlefield 4 on ultra settings at 1080p while getting 60+ FPS. You shouldn't really need much more than this, and it really took some money off of the final price by sticking with a 770. It's also decently future proof. Graphics card development has really slowed over the last couple of years, so I wouldn't really worry about this thing becoming obsolete.
Case - Antec Nine Hundred Black Steel ATX Mid Tower Computer Case with Upgraded USB 3.0
http://www.newegg.com/Product/Product.aspx?Item=N82E16811129021
Price: 99.99
You don't really need to blow a lot of money on the case, but I made sure to pick something out that was nice and rugged with plenty of airflow and a BIG side window so you can see all your beautiful equipment running smoothly
Plus it looks pretty sexy.
Motherboard - ASRock X79 Extreme6 LGA 2011 Intel X79 SATA 6Gb/s USB 3.0 ATX Intel Motherboard
http://www.newegg.com/Product/Product.aspx?Item=N82E16813157289
Price: 214.99
WOW are motherboards expensive. I had no idea. I was thinking of trying to stick it cheap with your motherboard at around $150 - $170 until i read some of the comments saying either the board died only a couple months after purchase or that the audio gave out. I decided it's probably better for you to spend a little extra just for the assurance that everything is going to work out nicely.
Power Supply - Antec TruePower Classic series TP-650C 650W 80 PLUS GOLD Certified Power Supply
http://www.newegg.com/Product/Product.aspx?Item=N82E16817371072
Price: 99.99
A really over-compensated part of a stereotypical PC is the power supply. You don't need anything ridiculous like a 700 or 800 watt unless you are planning on running Dual-SLI with Dual-CPUs or something. 650 watt should be perfectly fine for this setup. Also, going with a lower wattage than 700+ really saves money. This thing is gold certified as well, so it is going to run extremely efficiently.
Hard Drive - Seagate Constellation ES.3 ST1000NM0023 1TB 7200 RPM 128MB Cache SAS 6Gb/s 3.5" Enterprise Internal Hard Drive Bare Drive
http://www.newegg.com/Product/Product.aspx?Item=N82E16822178290
Price: 123.99
Again, I was going to try and keep it cheap with the hard drive. Again, all the reviews of the cheaper ones say they died after a short period of time. You really get what you pay for here, and I would rather spend a little extra if I were you just so you know it is going to work. You also don't need a 2TB hard drive. Nobody ever uses 2,000 Gb.
RAM - Crucial Ballistix Sport 16GB (2 x 8GB) 240-Pin DDR3 SDRAM DDR3 1600 (PC3 12800) Desktop Memory Model BLS2KIT8G3D1609DS1S00
http://www.newegg.com/Product/Product.aspx?Item=N82E16820148545
Price: 149.99
I don't know. 16Gb is a little insane when it comes to a gaming PC, and I think it can be easily over-compensated. Most games (to my knowledge) don't ever use more that 8, but if it's what you want, it's fine.
Monitor - AOC E2260SWDN Black 21.5" 5ms Widescreen LED Backlight LCD Monitor 200 cd/m2 20,000,000:1
http://www.newegg.com/Product/Product.aspx?Item=N82E16824160155
Price: 99.99
Just a standard PC monitor with a pretty decent screen size. It also runs at 1080p, so you'll get the full HD benefit of your GPU. The only downside is that it uses DVI cable instead of TRUE Hdmi, so TECHNICALLY it's not the highest quality your graphics card can go. Don't let that turn you away, though. This monitor is about $100 cheaper than any Hdmi monitor, and for the price difference, the picture quality difference is barely noticeable.
Optical Drive - LG Internal Super Multi Drive 24X DVD+R 8X DVD+RW 8X DVD+R DL 24X DVD-R 6X DVD-RW 16X DVD-ROM 48X CD-R 24X CD-RW 48X CD-ROM
http://www.newegg.com/Product/Product.aspx?Item=N82E16827136270
Price: 19.99
What can I say? This thing plays/burns DVDs and CDs. Most games nowadays are digital download anyway, so I'm sure it will be used mainly for the OS install.
Operating System - Microsoft Windows 7 Home Premium SP1 64-bit - OEM
http://www.newegg.com/Product/Product.aspx?Item=N82E16832416806
Price: 99.99
That's right. You may have noticed something missing from ksarex's build. An operating system. It may be just me, but I think it's a little difficult to play on a gaming PC with out an operating system, and I don't think Ubuntu would cut it. Also, adding an OS to his build would put the price over $2000. Just saying.
Mouse and Keyboard - Logitech MK120 Black USB Wired Slim Desktop
http://www.newegg.com/Product/Product.aspx?Item=N82E16823126097
Price: 15.99
Again, there isn't much to say here. I didn't choose a super gaming keyboard/mouse because I'm assuming you are playing casually and aren't planning on joining a MLG tournament any time soon.
Speakers - Logitech S120 2.3 Watts (RMS) 2.0 Speaker System - OEM
http://www.newegg.com/Product/Product.aspx?Item=N82E16836121013
Price: 14.99
Yet another thing missing from the previous build. I'm assuming you don't have any speakers currently, but if you do, you can just omit these from the final price.
Extra - Rosewill 6ft. DVI-D (24+1) Male to DVI-D (24+1) Male Digital Dual Link Cable, Model RCW-401
http://www.newegg.com/Product/Product.aspx?Item=N82E16812119012
Price: 9.99
You're probably wondering why you need the cable, and that's just in case one isn't included with the graphics card. There's one with the monitor, but it's VGA and I don't think you'll want to use that. Even if there is one included with the GPU, this will most likely be higher quality.
Total: 1659.87
HORRAY! We're in your price margin!
Just to wrap off, I want to clear up any questions you might have.
1. Why didn't I choose an aftermarket CPU cooler?
I read reviews of the CPU itself, and usually people let you know if you'll need aftermarket cooling on the stock CPU. In this case, there was no mention of it, unless you decide to overclock. With this CPU, overclocking should not be necessary though. It should last 5+ years stock, and if it does start to lag behind the competition, all you need to do is pick up a CPU cooler, some thermal paste, and overclock away.
2. Why didn't I choose an SLI setup?
This would have pushed you WAY over budget. If you are playing casually, you aren't going to need SLI with the GPU you have. I want you to keep in mind that the more cards you add to an SLI setup, the less power is taken from each card. Once again, though, if the card would, for some reason, start to become obsolete or you want to SLI anyway, you could just pick up another and slap it on since your motherboard is compatible (Up to 3-Way SLI)
3. Why didn't I choose an SSD?
At the time I'm writing this, SSDs are rather expensive for their storage sizes mainly due to the insanely fast write speeds. I'm assuming the prices will drop in the future when the technology is more widespread, but for now, a regular HDD will work fine. All it does is speeds up boot times of whatever you load on it, so if you are very impatient, you can pick one up, but for the average user, you can live without one.
For your own interest, I run a AMD Athlon X4 760k Richland 3.8 Ghz Quad-Core CPU and a Nvidia GeForce GTX 750 Ti on an MSI A55M-E35 Motherboard. I power it all with a Rosewill 635 Watt PSU (Which is extremely OP for my setup) and it's all tucked away in an Apevia X-Telstar JR case. I also lit it up with 3 Laser LEDs and have 3 hard drives totaling only 910Gb.
I guess if you have any price questions or some of the links don't work or something, just reply to me and I'll try to help you as quick as I can. If your mind changes on some of the things, *cough* RAM *cough* just reply and I can adjust accordingly.