YOU ARE ME.

I would grap a cheap set of headphones and spend the rest on games.

Spend a little more and get some Audio-Technica AD700s. Very popular quality phones for gaming.
Best SQ and soundstage (good for games) you can get for less than $100.
if that's too much, look at the not-as-good-but-cheaper-and-still-well-regarded JVC HARX900s
I'd stay away from "gaming" headsets, you will not get sound quality comparable to a decent set of standard stereo headphones at the same price.
But remember you will not get the best results with a crappy integrated sound card, make sure you have a decent source before you start spending significant cash on phones!

Oh yeah, I use the JVC HA-RX700. Very inexpensive, yet of the highest quality. Best pair of headphones I've ever used.

I have a wonderful pair of noise-canceling Seinheisers that my father gave to me (He upgraded to a more expensive pair). He takes many airplane trips, so a pair that can block out airliner noise is a must for him. My only gripe is that the noise-canceling bit is stored in a little box you clip to your belt, and the volume controls are a little too easy to accidentally mess with when you're running or when you put the headphones in a bag to travel somewhere.

Well now that you mention it. I am using an integrated sound card :S. What's good on the market, but inexpensive? Last time I researched, Creative had problems with their X-Fi cards.

I'd go for Steelseries 5H v2 instead. They're a bit heavier, but they don't look like a retard safety-helmet.
http://www.steelseries.com/int/products/audio/5hv2/information

The best headphones I've ever bought have always been $20.
Go figure.
Try that! You might be surprised.

Don't listen to that...integrated sound is more than adequate these days.

Thanks. I was thinking, after all, this is what I'll do first: get a good headset this weekend, then see if it will suffice.

I like my Sennheiser HD 280 pro. Don't leak sound[1], keep noise out, and sound good [2], especially for their price point.
[1] If sound leak is not a concern to you, there's better things out there for the same money. Personally - I use headphones because I don't want to bother others / for things (editing sound and the like) where it's important to really concentrate. They grip tight, which is where the noise reduction comes from, but are, I think, comfortable for long hours of wear, imo. I'd definitely recommend to try them on for some time before buying.
[2] These are, actually, proper monitor headphones. So no artificial bass boosting and the like. Not everyone likes the sound they produce, thus, but - well, I DO.

Personally, I've found that the best headphone purchase I've made on a value basis was a set of Koss PortaPro headphones.
No doubt that you could do better for a more money, but I've been really pleased with my set.
I'd encourage a purchase in the sub-$50 range to see if you can be happy for less money before you head too far up the price ladder (coming from someone who has spent way too much money on headphones).
Good luck. Let us know what you decide.
Edit: Grammar Fix (was typing it on my phone originally)

Lol a good friend was recommending these too.

I will probably be getting these:
http://www.bit-tech.net/hardware/peripherals/2010/09/11/corsair-hs1-review/1
The maker doesn't have any experience in audio equipment prior to this set, but it really looks like they nailed it. I'm just worried if I will be able to adjust after using wireless headphones for several years :P
And like someone said, stay away from razer headphones, 5+ of my friends who got them have nothing more than a tangled mess of duct tape left of their headphones. >.<