Noise often depends on what sound card you record from. I have a als100 sound blaster clone card which is very noisy, and a SB16 card which is a bit noisy, but much better than the former.
One thing that will reduce noise is to lower the voice audio volume to zero in the sound card's mixer utility (and disable voice audio in the games that allow it). Other things that could theoretically lower the noise is to lower other inputs and outputs you aren't using, like line-in and PC-Speaker. Can't personally say I've noticed any differences by doing this.
Also make sure the sound card you record with isn't part of the noise problem. If you want good recordings I would recommend to get a card suited for recording. If you are using sound blaster or similar make sure to use the line-in and not mic. I would stay away from built in sound cards.
Noise filtering does alter the music in a negative way. It's not something I would recommend.
If you want you can compare the recordings I've done in my signature and see if you get similar results. I use Audacity for recording and amplify most tracks 5-10x. Midi and master volume set to two steps from max in the SB16 mixer. Volume knob at back of the card to max.