My suggestion:
CPU: A
core i5-3570k will supply all the gaming CPU power you will need, but if your budget allows it, a
core i7-3770k is as good as you can get without going extreme.
Motherboard: A good
Z77 motherboard (such as
this one or
this one) will serve you well and allow for the best overclocking.
CPU cooler:
A Hyper 212 Evo is cheap and effective.
GPU: Yes, a
670 windforce will chew through Skyrim with no problems. However, a
HD 7970 windforce is around the same price, and offers better performance in nearly all games (including Skyrim)
Memory: 8G of ram should be plenty, however if you want 16G then go for it, just make sure it is decent quality
PSU: A good
650 watt PSU will give you heaps of juice for a single graphics card, however a
750 watt will leave some headroom if you ever plan to get a second. *****GET A QUALITY POWER SUPPLY**** Make sure that it is at least 80 plus bronze, preferably 80 plus gold. Cheap power supply's draw more power from the wall, and aren't as safe for your system.
SSD: A must for system these days. The
OCZ vector is about as good as you can get, and it's capacity is up to you and how much you are willing to pay. (128G is a good capacity for a boot drive and a few programs)
HDD: Again, how big your HDD is depends on how much you are willing to pay. Just make sure it is a quality one and that it is 7200rpm.
Optical drive: A cheap optical drive will serve you fine, but you will have to pay extra if you want to watch blue ray disks on it.
Case: This is left much to personal preference, as aesthetics vary greatly among different cases. Corsair and Cooler Master cases are my personal favorites, as both offer nice looks and great cooling. Choose one in your price range.
Without budget, it's difficult to recommend specific parts, but hopefully this gives you something to work with.