This article will help you determine whether your current PC can run Mac OS X. However, if you're looking to build an entirely new computer for Hackintoshing, the easiest route is always to follow tonymacx86's CustoMac build recommendations, or our own list of cheap Hackintosh builds. If you don't want to build your own computer, check out our 2012 laptop buying guide, or our overview of the Dell XPS 8300 (which is pretty much the only well-documented, prebuilt desktop Hackintosh).
Self-Built Computers
Motherboard:If your computer's motherboard was designed for Intel processors, and was manufactured in 2010-2012, there is a pretty good chance that it will work with Mac OS X. Motherboards made before 2010 are a lot trickier to work with, and may not be worth the effort.
Brand-wise, motherboards made by Gigabyte are the best-supported, since they're the only boards that work by default with the CPU power management service built into Mac OS X. Older Gigabyte motherboards have DSDT files available in the DSDT section of tonymacx86, which are immensely helpful. DSDT files are configuration files that make Mac OS X to work with your specific motherboard (the DSDT for one motherboard will not work with another motherboard). The newest Gigabyte motherboards, which use UEFI instead of BIOS, don't even need a DSDT file.
If you don't have a Gigabyte motherboard, check out tonymacx86's DSDT section to see if they have a DSDT for your motherboard anyways. If tonymacx86 doesn't have the right DSDT file, consider patching your own DSDT file with DSDT Editor. If your non-Gigabyte motherboard uses UEFI, it won't need a DSDT file; however, it will still need a patched BIOS file to work fully.
Whether you have a Gigabyte motherboard or a non-Gigabyte motherboard, be sure to search Google for specific Hackintoshing instructions on your particular motherboard. For example, if you have a Asus P8Z68-V LX Motherboard, then search "P8Z68-V LX hackintosh" on Google. Besides Gigabyte, ASUS is the second most popular motherboard brand for Hackintoshes, so you can often find a lot of Hackintoshing guides about ASUS boards on Google. You might also find Hackintoshing guides on motherboards from other brands, but they are far less common than guides for Gigabyte and ASUS boards.
Graphics card: Besides the motherboard, this is probably the most important part of your build. Mac OS X often does not work with the built-in ("integrated") graphics on motherboards or CPUs. In those cases, you will have to buy a separate graphics card for your computer. The only exceptions to this rule are the built-in graphics cards of Intel Sandy Bridge processors and Intel Ivy Bridge processors; you can check the CPU section below for more info.
Older graphics cards (like the NVIDIA 8800GT and AMD Radeon 5770) will usually work with Mac OS X "out of the box", without the need for any extra drivers or modifications. As far as newer graphics cards go, most cards in the AMD Radeon 6600 and 6800 series will work in Mac OS X out of the box, as well. Some cards in the NVIDIA 400 series also work out of the box, but most of them require you to install OpenCL Enabler in Multibeast (for Lion and Mountain Lion), or the official NVIDIA drivers (for Snow Leopard).
Cards from the NVIDIA 500 series work with Mac OS X Lion and newer, while cards from the 600 series work with version 10.7.5 of Mac OS X Lion and newer. To enable graphics support for a 500-series card in Mac OS X Lion, you have to install OpenCL Enabler in Multibeast. In OS X Mountain Lion, the 500 series and 600 series work out of the box, though you have to use the boot flag "GraphicsEnabler=No" (without quotation marks).
Cards from the NVIDIA 700 series work in version 10.8.3 of OS X Mountain Lion and newer. However, the cards don't work "out of the box"-- to enable graphics support for a 700-series card in Mountain Lion, you have to install NVIDIA's latest graphics drivers for Mac OS X (version 313.01.01f03 or newer). You also have to use the boot flags "GraphicsEnabler=No" and "nvda_drv=1"(both without quotation marks).
The AMD 7000 series also received support in OS X Mountain Lion 10.8.3. Most of the graphics cards in the series work out of the box, though the setup process for these cards is still harder than for the newest NVIDIA cards.
The AMD 6900 series isn't supported (and probably never will be). Additionally, ATI CrossfireX and NVIDIA SLI, which allow you to run two separate graphics cards as a single graphics card on Windows, do not work on a Hackintosh. Mac OS X will always recognize double-card setups as two separate graphics card.
Mac OS X can be very picky about graphics cards; the manufacturer of the card matters just as much as the card's model. For example, a Gigabyte Radeon 5770 graphics card might work differently from a Sapphire Radeon 5770 graphics card. In addition, when we say that a particular graphics card series is compatible, this doesn't necessarily apply to every single card in the series. Oftentimes, lower-end graphics cards and mobile graphics cards in these series don't actually work, for a variety of reasons.
Before buying a specific card, always check Google first; for example, if you want to check the compatibility of a Sapphire Radeon HD 6850, search "Sapphire 6850 hackintosh" on Google. It's easy and saves you a lot of trouble.
CPU: Almost any 2010-2012 Intel CPU will work with Mac OS X. AMD CPUs are barely supported, and therefore not recommended. Older Intel CPUs can usually run Mac OS X Snow Leopard, but many don't work with Mac OS X Lion or OS X Mountain Lion. Lion and Mountain Lion are 64-bit operating systems (x86-64), so they're incompatible with the 32-bit architecture (x86) that older CPUs use.
The Sandy Bridge generation of Intel Core processors is supported by all recent versions of Mac OS X, including Snow Leopard, Lion, and Mountain Lion. Sandy Bridge processors are the processors with a model number in the 2000's, such as the Core i5-2500. They include built-in graphics cards that work with Lion and Mountain Lion (but not Snow Leopard), and come in two versions: HD 2000 and HD 3000. Unfortunately, only HD 3000 graphics are officially supported. HD 2000 sort of works, but it doesn't have graphics acceleration, so it's not recommended.
The Ivy Bridge generation of Intel Core processors is supported by Mac OS X 10.7.5 and all versions of OS X Mountain Lion. Ivy Bridge processors have a model number in the 3000's, such as the Core i5-3450. Ivy Bridge is not supported by Mac OS X Snow Leopard; while you can still technically install Snow Leopard, CPU power management does not work. They also include built-in graphics cards, which come in two versions: HD 2500 and HD 4000. HD 4000 graphics work with OS X Mountain Lion and Mac OS X Lion (version 10.7.5 and above). HD 2500 graphics work with OS X Mountain Lion version 10.8.3 and higher.
Intel's newest Haswell processors are not fully supported in Mac OS X yet. Haswell processors have a model number in the 400's, such as the Core i7-4770.
P.S. Intel Sandy Bridge processors don't work very well with Mac OS X Snow Leopard version 10.6.8. I recommend that you update to version 10.6.7 instead. You can still update to Mac OS X Lion from 10.6.7 (Mountain Lion requires 10.6.8, but you might be able to circumvent this requirement by spoofing your system version).
For more detailed information, check out our guide on Hackintosh CPUs.
And the rest: Most WiFi adapters and WiFi cards don't work with Mac OS X. Using a wired internet connection with a Ethernet cord is preferred. If you need WiFi, check out MacBreaker's list of natively-supported WiFi adapters.
While most Bluetooth adapters technically work with Mac OS X, a large majority will break sleep mode. If you want to use a wireless mouse that needs Bluetooth (such as the Apple Magic Mouse), but you also want to use sleep mode, check out our list of recommended Bluetooth adapters.
Most hard drives should work fine, though there are occasional exceptions. Hard drives with 4096 byte sectors (instead of normal 512 byte sectors) have problems booting Mac OS X, and need a rather complicated Terminal fix. This issue is most common in Western Digital Caviar Green hard drives. Seagate hard drives are generally problem-free in this regard.
Just about every solid state drive (SSD) will work with Mac OS X by default. However, some SSDs don't have built-in garbage collection services, so you'll need to enable TRIM in Mac OS X by yourself.
Additionally, some optical drives may prevent Mac OS X from sleeping. If you want a safe choice, buy a from a confirmed DVD drive series like Sony Optiarc. Hackintoshes can read and write Blu-ray discs with a Blu-ray drive, but you can't play Blu-ray movies because they don't support Mac OS X.
If a webcam claims to be compatible with Mac OS X, then it's likely that it will work for Hackintoshes too. (Note that most webcams will not need drivers to run on OS X.)
The same goes for any other peripherals, such as mice and keyboards: most of them work, but you can never know for sure until you've tried it.
To check the compatibility of specific peripherals, be sure to check with Google. For instance, if you want to know whether the D-Link DBT-120 is compatible with Mac OS X, search "DBT-120 hackintosh" on Google.
Pre-built desktop computers
Okay, so maybe building a new computer isn't an option for you. It's definitely possible to turn a normal pre-built computer into a Hackintosh. It's just not very likely. If you want to attempt an install of Mac OS X on a pre-built computer, you need to do your research beforehand.
The main problem with pre-built computers is that they have really weird motherboards. When building PCs, manufacturers tend to use their own proprietary motherboards that nobody has ever heard of, so nobody has ever had to chance to make them compatible with Mac OS X.
You will have to search Google for specific Hackintoshing instructions for your particular model of computer. For example, if you have a Dell Optiplex 745, search "Dell Optiplex 745 hackintosh" on Google.
If you can't find a Hackintoshing guide (or wiki entry) for your desktop computer model, then the Hackintoshing process becomes a bit of a crapshoot. If your computer is a relatively new model and uses an Intel processor, there's a chance that it can run Mac OS X reasonably well. You will generally have the best luck with gaming PCs from small "boutique" manufacturers (like iBuyPower or CyberPowerPC), since they tend to use publicly available motherboards. However, without the help of a guide, I can't make any guarantees.
Laptops
The same rules for pre-built desktops apply to laptops: search Google for specific Hackintoshing instructions for your laptop model.
And good luck Hackintoshing.