Obviously you should spend the bulk of your budget on a video card.
(usually about 1/3 of your total budget if you are going for a strictly gaming pc.)
If you need to cut back i would do it on the Hard Drive. You can always buy more space latter when you have the money.
The Memory and CPU are both very important components but the memory can usually be bought cheaper if yo go with a slower speed. Example: 4gb of memory will take care of just about anything you need. If you go with 1333mhz instead of 1600mhz you will save some money and you can overclock the 1333mhz to be
The CPU on the other hand you dont want to cut back to much. You can save a few dollars by going with something like the i5 750 instead of the i5 760 and overclocking the i5 750.
You can usually save some money on a mother board if you go with the lower end board of a Good brand name. In most cases you can get all the features you need with out the extras you don't.
The CD/DVD is another area you can cut back on. You can get a Decent cd drive for under $20. No need to spent alot of money here.
When building a PC start with the CPU. Decide which one the PC will be base around. Here is where you can get the lower clocked little brother of the mainstream chip for cheaper and OC it to the same speed. i.e. Getting the i7-950 instead of the i7-960, or the AMD 955 instead of the AMD 970. I say if the jump to the higher card is less than $10, you might as well do it. More than that, it's something to consider but not required.
Motherboard, I wouldn't skimp here. This is the backbone of your PC. Sure "just any" board will work but find one from a decent line of boards and get the lower versions. i.e You probably don't need the Asus P7P55D-E PRO and the P7P55D-E LX is just as good but the LX one is $60 cheaper. Only get what you need and will use, there's no point paying for features you never look at again. Cheap boards usually severely limit your expandability and overclocking capabilities. If you don't plan to upgrade and don't OC then by all means get the cheaper board, but stick with reputable name brands.
RAM is also a place to look. Do you really need CAS7 ram? or DDR3 1600? People can't really tell the difference in improvement past DDR3 1333 CAS9 RAM, only benchmarks can.
The same reasoning can be applied to the GPU. Do you really need all that power? You only really need low to medium settings to actually enjoy the game as long as it's not choppy ot laggy, but you can enjoy it more at high to max settings. This is really personal preference and how much you want to spoil yourself. SLI? CF? That's pushing it a bit. Most games are already maxed out with a single high end card. Two of them really only improve benchmarks. You won't be able to tell the difference in actual gameplay but if you freeze frame it and look very closely you might see some differences.
Just about everything on the PC has a little brother you can get for cheaper. Some parts you should consider if you even need it at all, like the ODD.
One think you shouldn't skimp on is the PSU, always buy a high quality 80+ certified PSU of a reputable name brand. I don't mean to spend $200+ on one, a Corsair 650W TX series is usually around $70. Don't give a cheap no-name PSU the chance to destroy your PC when it fails, just don't use them.