...to run a computer with an Athlon 64 x2 3.0 GHz, a GeForce 8800 GT, and 4 GB of RAM? I know there's other things to take into account, but that's gonna take up the majority of it. It will only be running 1 hard drive and 1 optical drive.

way more than enough. I have a 450 watt power supply and run an intel core 2 duo, 8800GTX, 3GB RAM and have two hard drives, dvd burner, etc. the GT is probably more power-friendly than the GTX.

It should be enough.

The problem with PSUs it seems (I have been informing myself on the subject 2-3 months ago because I was building my own system for the first time) is that an X-watt PSU is not enough for a computer consuming X watt. You have to take into account the different rails and how power is divided among those. During my search I collected a few PSU-related pages, maybe they can help you further (the power supply calculator especially (the 8800GT consumes less than the 8800GTS, so in case the calc does not list the GT, pick the GTS for a conservative approximation)), but they mostly just make you doubt more than you already do now. In case you care, I am under the impression one big 12V rail (60A) is the better choice these days.

To give a definite answer to your question, I believe a 650W should be more than enough.

(I also have a 8800GT, be aware that there might be a bug in its bios that makes the fan stay on 29% regardless of the temperature... but there's a really good chance (90+%) that this issue has been fixed by now. I, having bought the card end november '07, am stuck using RivaTuner to keep temperatures in a reasonable range).

I have an OC Q6600, 8800GTS, 3Hdds, 1 optical, 4gig ram running off a Corsair 620W . Needless to say, it is rock solid.

So unless you are putting a shit load of HDDs in there, you should be fine from what I understand.

I've used that power supply calculator on my own machine just for fun, and according to it, I can't run my own hardware. I got a crap 250w PSU, and according to this, I need about 100 more at minimum. [lol]

Either it's bugged, or it overcompensates.

Moved to Hardware Discussion. We do still have that thing.

For comparison: I have a Core 2 Duo E6850, 4 sticks of 1 GB CAS4 DDR800 RAM, a GeForce GT/512, a Live! X-Fi sound card, two 10,000 RPM drives and a 7200 rpm drive, aome number of 5" fans and a slew of USB devices. My machine draws 100 watts when sleeping, 160 watts when idling, and 250 watts when playing Crysis (64-bit). This is measured using a watt meter at the outlet. I have a 470 W power supply, which is more than enough. I'm a little annoyed at the high draw when sleeping; other than that I think it's fairly typical.

If you buy a power supply that's designed for a higher draw than you pull from it, it will not be as efficient, and it will end up wasting energy, which means a higher energy bill and a warmer room. Also, try to get an "80 plus" certified power supply to make sure you don't waste too much energy into heat.

If it's a high quality PS 650W is more than enough and I"d say overkill especially with today's highly efficient cpu's,gpu's,green harddrive,etc.
For comparision I'm running all of the following in my main system on a 500W Antec power supply:
Intel 6600
Evga 8800GTS 320MB not 256MB--really that's a Vista bug!
Kingston valueram 553mhz ddr2 3GB
Asus P5NSLI
SB X-Fi Xtremegamer
Plextor sata px755sa burner/Memorex IDE DVD burner
150GB and 74GB raptor drive
2x500GB seagate sata drives
P180 with Antec 550W PS
WinXP/Vista Ultimate 64 dualboot
+ numerous external usb/firewire drives