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Budget: Intel Celeron G540 - dual-core, 2.5GHz
Nowhere near as attractive as the Core i7-3970X Extreme Edition, but the Sandy Bridge-based Celeron G540 is a great choice for those looking for those looking for a cheap processor.
Along with a solid 2.5 GHz processor, you will receive on-board Intel HD graphics, which means that you don't need a separate graphics card. It's not going to run Crysis 2 with all the options turned up to the max, but it's a fine general purpose GPU.
Image source: Intel.