You'll need a Power Supply, motherboard, Processor, and Memory. Those are the bare essentials.
Following on from that because you want a gaming system, you'll probably want a new graphics card, and new sound card since the ones that usually come on motherboards don't do anything justice.
MOTHERBOARD AND PSU:
It depends who you would like to go for in the motherboard and PSU department since there are loads of companies, but of course some are better than others, but many are just as good, and many people prefer different makes.
Motherboards though come with different features that you might want and might not want, for example a sound chip (though most contain one anyway), firewire (tranfer video and data in this high speed port), USB2.0 ports (essential, but motherboard sometimes have more slots than others)
With Power Supplies (PSU), the only thing you have to watch out for as well as make of course is the wattage given out by the supply, and an excellent gaming system might need a 500watt, or even a 600watt if it has alot of components, though many computers including mine does fine with a 450watt, and this would be the standard nowadays I would think.
Memory is the same really, with alot of companies, but for a gaming machine, I would definetly opt to get dual channel RAM (A special type of ram which speeds up memory and so the computer when 2 are used in one go in a motherboard that supports the ram) and get at least 1GB of it which will do you well (2x 512mb sticks) as most games are asking for this now.
With Processors, it's either AMD or Intel, and these can both be just as good, but again, they work better with different tasks.
AMD has been proven to be better at games than Intel, with there reletivley new Athlon 64 range of processors, against Pentium 4's.
Athlon 64's by the way are ready for 64 bit computing, so with going with that type of processor, you know your computer will be ready for the future when you decide to buy a 64 bit Operating System when more programs and games start to use the new process. Intel do also have a 64 bit platform now, but it is quite expensive. With Dual processors coming out now though, prices of these will drop.
With Graphics cards come Nvidia and ATI, both good again, and its mostly up to personal preference which you go for, because both are about the same in terms of games, though Nvidia seems to hold the gaming crown at the moment with many new cards (the 7800 series being the new and most powerful one out)
For sound, i'd go for Creative since they hold the crown and have been making sound cards for ages, with the Audigy ZX 2 being the newest card I think offering 8 channel surround sound? Anyway, if this is not what your into, you can get a more budget one allowing for maybe 5.1 which is always good for movies as well as games if you are into getting a DVD drive.
Anyway, I hope I have helped in deciding what you might want to go for and you can now do some research into which companies you might like, etc
Hope I've helped