I'm building this for gaming. My budget is at most $800

I want it to play anything above average settings.

thoughts?

Intel® Core™ i5-3570 Processor (4x 3.40GHz/6MB L3 Cache)
Liquid CPU Cooling System w/ 92mm Radiator [Intel]
8 GB [4 GB X2] DDR3-1866 Memory Module
AMD Radeon HD 7870 - 2GB Single Card
Gigabyte GA-B75M-D3H
1 TB HARD DRIVE -- 32M Cache, 7200 RPM, 6.0Gb/s Single Drive

Above average settings, hmm?
Try any game at max at a resolution of 1080P, might aswell throw in 4xAA for good measure too.
The Radeon 7870 is *very* similar in performance to my old Radeon 6970's in terms of performance.

However, get the K edition version of the i5-3570 processor so you can overclock or drop the Liquid cooler and get the Coolermaster Hyper 212+, no point having that combo otherwise.

Also, if you can afford it, jump on the Radeon 7950. :)

Also, what Power Supply do you intend to go with?

A standard 500 Watt would do good I think. Isn't the 3570k missing some abilities?

Nah, the 3570K is the unlocked version that lets you overclock, otherwise it's the exact same as the vanilla 3570.

Also, if it's a "standard" 500w PSU, aka, not a brand name based on a CWT/Seasonic design, then I would seriously look at something better, something like a 650w Corsair TX/HX, Antec Neo Eco 620C, Enermax NAXN 600W, Seasonic M12II etc'.
The PSU is the most important component in a PC, some of the cheaper brands/models lack protection mechanisms like over-voltage protection, bad filtering, low gauge wiring, low efficiency etc'.
Best to just get a quality unit now with a good warranty which you could bring over to your next PC, the Corsair HX units for instance have a 7 year warranty, so it wouldn't surprise me if it outlived a PC or two.

Hmm I see. Good advice.