I poked around because I'm also looking at a budget build, and came up with this for under 800 bucks.
CPU: Intel Core 2 Duo E8500
Motherboard: MSI P45 Platinum
RAM: Corsair Dominator 4GB (2x2GB)
Power Supply: Corsair 750 Watt
Graphics Card: ATI Radeon 4850 (Sapphire Dual Slot)
Case: Raidmax
As for a hard drive, that depends on your storage needs, in terms of music, pron, games, etcetera. A 7200RPM from a brand like Western Digital or Seagate will be sufficient, and you can find good deals.
I'd roll with dual core because those extra cores aren't often utilized effectively by most programs today. Plus, when it comes to gaming, a faster-clocked CPU, and a powerful graphics card are what you need. By the time multiple cores are worth it, you'll need a new computer anyway.
The motherboard has also gotten rave reviews, and it'll let you Crossfire ATI cards if you wish. Two 4850's running in CF will let you up the ante, and get good framerates in resolutions at 1920x1200, which is a pretty big montor. It'll let you use an Nvidia card too, but only one.
The power supply is also a great, reliable performer, which is a big deal today, and it'll let you have some future expansion. Also, the case is a good one; I own it, and it's great to work with, although the lighting can be a little 'ricey' but at this price, you're crazy to go with something else.
If you aim to overclock now or in the future, the CPU, the Motherboard, and the RAM will let you go nuts; with a decent third party fan, you should be able to easily get that E8500 runnning at 4GHz.