Build above is absolutely fine, and more or less what everyone is going to suggest, with a few changes here and there.
Main thing will be - what does your $1500 have to include? If it's just the case and components, you have a massive budget to play with. If it's got to cover monitor, OS and perhaps peripherals, then you still have a healthy budget but you might need to cut back a few things.
Regardless of these things, i5 3570K will be what everyone suggests. If you really don't fancy overclocking then save yourself a few $ and get any Ivy Bridge i5 (3xxx), their performance is pretty damn similar for games if you aren't overclocking.
With that amount of money to spend it's likely you'll have at least $300 to spend on graphics so the GTX670 and HD7970 are likely to be in your price range. If you are only intending to play at 1080P you can drop that budget a bit and not really loose much.