There are other computer processor brands outside of Intel and AMD indeed, but it good to narrow down the discussion to these widely popular names. They are easy to find and the compatibility factor is basically better than others.Intel Core
When building a Hackintosh computer, most people will simply choose Intel over AMD for a very good reason that we call “compatibility”. Any of the latest generations of Intel processors called Intel Core works with Mac OS X, and therefore it works with Hackintosh equally well. Intel Core processors including the Sandy Bridge (2nd gen), Ivy Bridge (3rd gen), and Haswell (4th gen) have been proven to work properly with Hackintosh; Broadwell (5th gen) has just arrived. However, the most sophisticated processors of the Core family including Sandy Bridge-E, Ivy Bridge-E, and Haswell-E are not completely compatible with Hackintosh due to the use different sockets.
Intel Celeron and Pentium
Some of the older generations of Pentium and Celeron are supported in Mac OS X. The bad news is that the newest Celeron and Pentium from Haswell generations are not supported in this operating system as well as in Yosemite. If you are trying to cut cost when building Hackintosh, Celeron and Pentium are not actually bad ideas. The underlying architectures used in those mid-range processors are mostly similar to those implemented in Intel Core. Either Ivy Bridge or Sandy Bridge uses LGA1155 socket which is the same with Intel Celeron G530. Therefore, a Hackintosh powered by G530 works well.
Mac OS X is a 64-bit operating system, so you need to use Intel Processors that support the architecture. Old processors such as Pentium M are simply too old for Hackintosh and mainly because they are 32-bit. There are of course some processors from around 2010 that work with Hackintosh, but you need to choose carefully.
The problem with installing Hackintosh on an AMD-powered computer is the kernel, an important file that allows all applications in Mac OS X to communicate with hardware. Mac OS X has vanilla kernel designed to work with Intel processors only. It is actually possible to install many versions of Mac OS X to AMD computers, but you have to modify the kernel. If you have no idea how to modify the file, your best bet is to avoid using AMD for Hackintosh at all. Even when you can and successfully modify the kernel for installation, your Hackintosh will not be as stable as when it is run on Intel-based hardware.
In most cases, using the latest generation of Intel Core (excluding Xeon) is a good decision when building Hackintosh machine. AMD is a possibility, but the installation and configuration after that can be very complicated, so you are better off without it.