I'm building my first budget gaming rig this week, and I need a little advise on what hardware is best to expand on, while saving money in other areas. For instance:
 
I could buy a Core i7-860 ($270) and get a 9800GTX ($140) for a total of $409. ((Sacrificing GPU for CPU))
OR
I could buy a Core2 Quad Q9400 ($190) and get a GTX 275 ($209) for a total of $399. ((Sacrificing CPU for GPU))
 
I could also downgrade both mentioned components in exchange for more RAM, etc.
 
So, my question is, what's the most important component these days? I know it used to be GPU, but I hear people talking about CPU and RAM more than ever. What's your input?

There is a lot of variation in a game by game basis, as well as if you're considering long term ease of use versus short term games.
 
GPU is more important, yet graphics standards aren't really being pushed.  I'd say for most games your Core 2 Quad Q9400 + GTX275 would be the far better performing computer.  However if you upgraded your GPU on the other computer in a year or two that one would be far better.
 
Some games like Supreme Commander or Grand Theft Auto 4 require a disproportionate amount of CPU power for optimal performance.

Well dual core is pretty much standard these days so that's sufficient. Quad core maybe too much but if you got the money I see why not.
If you're using vista than 4 rams is what you need if you're aiming for high performance.
GPU is fairly important. The hard part is just choosing which model really. Personally I found ATi cards to be reliable.
 
All three are important so try to keep a balance rather than favouring one over the other. 

Anything specific you want to know?

So a i7 build wouldn't outweigh a solid GPU?
 
Also, should I go for DDR3 or the old DDR2 stuff?

" So a i7 build wouldn't outweigh a solid GPU?  Also, should I go for DDR3 or the old DDR2 stuff? "

DDR3 sounds good. But if you're on a tight budget. DDR2 shoud last a few years until DDR3 becomes standard.
 
Also depending on the game in question the GPU or CPU could be more important.

" @PISTOLcm said:

" So a i7 build wouldn't outweigh a solid GPU?  Also, should I go for DDR3 or the old DDR2 stuff? "

If the computer you're building requires DDR3, go with that, if not DDR2.  

Also, should I go for the 64-bit Vista for System Builders?
 
Not sure what the difference is.

9800GTX would definitely underperform on a few of today's more graphically-intensive games.
 
 
I'm about to order a new computer myself. Going with a Dual Core and a GTX 275.

Also, should I go for the 64-bit Vista for System Builders?  Not sure what the difference is.

What mandates DDR3 use?

I'd say in 99% of cases the GPU is more important when it comes to running games. If games are all you are interested in then go with the better GPU.

Cpu at a high speed might help with less bottlenecking of framerates, which you can overclock if you know how. Also the gpu is more important obviously, it renders graphics. You could just get a i5 cpu, that's $200 on newegg.com and go with the gtx275.

Every part is important. But it's easier to upgrade things like the video and sound card and ram down the road so it's best to take the best and most futureproof motherboard, processor, case and power supply you can to begin with. The cpu is not less important to the GPU for games.

My shitty single-core processor is what keeps me from running a lot of stuff.

Rendering is done on the GPU. AI, other things (such as physics, sometimes), are done on the CPU. In games, GPU is more important. In non-realtime rendering, cpu is.

Sacrifice GPU for CPU and get a weak card right now. Later this season you should be able to find a better card for the same price.  
I have two 9800 GTX+ running in SLI and still get outperformed by single 200 series cards. I think ATI's 5000 series is coming out soon and it looks sweet.
 
Also RAM is cheap and SUPER EASY to install more when you feel you need it. Don't worry about that.
 
You don't wanna upgrade the CPU again for a long time because that'll probably mean a whole new system.

 Core i7-860 ($270) and get a 9800GTX ($140) for a total of $409. ((Sacrificing GPU for CPU))   

 Core2 Quad Q9400 ($190) and get a GTX 275 ($209) for a total of $399. ((Sacrificing CPU for GPU)) 

Seriously thinking about going for the GTX260, Core2 quad and 4 gigs of RAM.

 @HitmanAgent47:  The one I linked is a 216 :P

Yea I agree don't waste your money on a pre overclocked card.  I don't even think they build them at a higher production quality or anything.  I don't like overclocking anyways though, just makes stuff run hotter and your fans thus noisier.

" Yea I agree don't waste your money on a pre overclocked card.  I don't even think they build them at a higher production quality or anything.  I don't like overclocking anyways though, just makes stuff run hotter and your fans thus noisier. "

GPU is definitely the most important component for titles utilizing engines that took full advantage of high-level shader languages when they originated. Examples would be id Tech 4 (Doom 3, etc.) and Unreal Engine 3. I would consider this the majority of the market at this time. 
The exception to this rule is engines like Source that did not originally make extensive use of high-level shader languages; these titles are typically CPU-limited but not terribly; a good GPU is still the top recommendation. 
 
I suspect there will be a price reduction on current-gen GPUs in the near future as DirectX 11 GPUs are finally released. The ATI HD5000 series is due next month and while I haven't heard much news on the nVidia front, their response is likely to at least reduce their existing GPU's prices to remain competitive.