I'm getting a new computer soon and was wondering when they have computer systems for the "Serious Gamer" what sort of games qualify as needing that system to play well?

Here's a better question for you to think about: What kind of game do you plan on using the computer for? If it's only going to be games on here or anything before 2005 or so, your goal line is Witcher 2. If it's going to be modern games in the mix, your goal is going to be Farcry and Crysis.

So with your logic i'm not a serious gamer cause I don't like Battlefield 3? That sounds kinda lame don't you think ;)
Damn this youngster only see graphics in games...

What about the below build: (price $990.21)
HP Pavilion HPE h8m customizable Desktop PC
A5U01AV#ABA
Genuine Windows 7 Home Premium [64-bit]
AMD FX-6100 six-core processor [3.3GHz, 6MB L2/8MB L3 Cache]
8GB DDR3-1333MHz SDRAM [2 DIMMs]
1TB 7200 rpm SATA hard drive
Microsoft(R) Office Starter: reduced-functionality Word & Excel w/ ads. No PowerPoint or Outlook
SAVE $30 on Norton Internet Security(TM) 2012 - 15 month
1GB DDR5 NVIDIA GeForce GTX 550 Ti [2 DVI, mini-HDMI. VGA adapter]
600W Power supply
SuperMulti DVD Burner
Integrated Ethernet port, No wireless LAN
15-in-1 memory card reader, 2 USB 2.0 (front), audio, 2 USB (top rear-facing)
No TV Tuner
Beats Audio (tm) -- integrated studio quality sound
Premium HP keyboard and optical mouse

3 issues with that build... 600W power supply ? MS Office? and without a SSD for the OS?

Does "serious gamer" here mean someone who spends a lot of money for their HW (and games), or someone who e.g. plays challenging and time-consuming games?

Those two are not quite the same. Usually, when people buy a brand new PC (or console), they are more inclined to buy more, especially flashy and new, games for it, just to demonstrate what their new machine is capable of. So when I eventually get a new PC, I will probably want to demonstrate its capabilities by running the most graphically demanding games, whichever they might be (Crysis 2? Witcher 2?). The gameplay etc. is a secondary issue at that point, I wouldn't select Master of Orion even if I thought it is overall a better game than either Crysis 2 or Witcher 2.

When the machine is not that new anymore, they might start choosing their games with different criteria, e.g. GOG games. :) (apart from Witcher games, I guess)

Last I heard, Metro 2033 was the benchmark but I could be wrong now.

What is the issue regarding the power supply????

Too expensive, and all the parts relevant for gaming are a notch under the performance you'll want. Aim for at least an nVidia 560 GTX graphics card (preferably a 560 GTX Ti). The CPU's performance is extremely disappointing - review sites attest even the Pentium G860 better gaming performance, and group it together with Core 2 Duos. Get an i5 2500 if you can afford it (should be possible if you're looking in the 1000$ price range), or an i3 2100 if you can't. You can also go with faster memory (memory is cheap now), though there won't be much of a performance increase. Finally, drop Microsoft Office unless you really, really need it - it makes the build more expensive, but Open Office gets the job done just as well, and costs nothing.

The normal PSU for nowdays computer is 750+W. Everything less is weak ;)

You dont really need an SSD for the OS, yeah it will boot into Windows really quickly but its not good if you are going to be installing and removing games / files from it often. I decided against when I did my new build last year, they are still pretty new tech and expensive for what you are getting.

MS Office isnt overly essential either if you dont use office programs that often, I would suggest for an occasional office user to get Open Office, it supports all the MS documents etc

When it comes to games to push the system with the Nvidia 5 series cards or the ATI 6 and now 7 series you want to be looking at the stuff with Direct X 11 Tesselation. This includes games like Crysis 2 (You have to download the DX11 patch and high res textures manually), Battlefield 3 running on Frostbite 2 engine, Stalker Call of Pripyat, Metro 2033 to name but a few.

I am running a Phenom II X4 965 Black Edition, 8 Gb Corsair 1600 Ram, MSI GTX 570 Twin Frozr 3 OC Edition, 1x 500 Gb SATA (For Windows installation), 1.5 Tb SATA, 750 Watt Antec True Power Modular supply and a 1920x1080 Asus LCD.

Everything runs smooth as silk in 1080p resolution and maxxed detail setting with FXAA & MSAA enabled. I did start with a 560 TI but it had faulty ram and I was getting loads of artifacts, however before it became faulty was running everything fine.

Sound advice, and this is coming from someone who currently runs an AMD chip.

What on Earth are you powering with that? That's overpowered as hell. And considering PSUs are most efficient at about 90% of their nominal maximum power [citation needed], it's also very wasteful.

I've got a pretty decent gaming build and I've got a 400 or 450 Watt PSU (can't remember off the top of my head). Never had a problem.

3 x1TB hdd + 1SSD + quite good VGA...