From my answer on the When will dual core android phones start to become available? question, there's a good comparison of the HummingBird vs SnapDragon processor systems here. Hummingbird is a system made by Qualcomm and used in phones like the Nexus One and HTC Desire, the Snapdragon is made by Samsung and used in devices like the Galaxy S and Galaxy Tab. OMAP is another system chip brand, this one by Texas Instruments and used in phones like the Motorola Droid and the Palm Pre.
All of three of those are "System on a Chip" systems, where the CPU, some memory, and some other processors like the Graphics Procesing Unit, digital signal processors or wireless signal processing unit are all built into the same chip. Building all of this into a single chip instead of having all the individual capabilities spread out across separate chips gives a lot of savings in power usage, size and space used inside a phone.
The CPU inside all of them uses the ARM processor architecture, which is a standard set of instructions and abilities that the CPU follows. As do the iPhone's processors, the iPhone 4's processor is also made by Samsung and is very similar to the SnapDragon processors used in Galaxy S's. Other processor architectures that you may have heard of are the Intel x86 processor architecture, or the AMD64, one of which is probably powering the machine you're reading this at.