Welcome to the world of Electromagnetic Interference.
Sounds like the hum on any normal computer mo-bo.
Purchasing an external interface will probably help.

What is your current gear? Audigy?

i am with greener. can you post a longer clip with the actual music recorded? there are software plugins that can help in cleaning it up. it can also make things worse if overdone.

I just want to record my voice with the mic I have with as little interference as possible. What software would you recommend to do the job of minimizing the interferences?

How is software going to combat random electrons being forced to move due to magnetic interference? The affect is not something you can hide, you need shielding, you need to move the analog part of the equation away from that noisy powersupply and motherboard... You need freedom. Cast off the shackles of onboard mic pre's and hunt out the Interference Demons.

Seriously though, get an external interface. You can get ones for under US$100 that sound clean.

Why edit the sound away with a $1000 piece of software when you can just not record it in the first place?

once again, i am with you greener. yes, you need to address the issue so you don't have to deal with same problem down the road. the software comes in only if the recording is a keeper and you have no other way to do another take. there is a tool for almost everything.

for $240. you can get izotop RX software or, for the same price, an M-Audio FireWire 410 (or some other brand). i would go for the audio interface if i were you.

FYI Windows Sound Recorder is an excellent program. It does the job, doesn't it?

Your soundcard is causing the noise, not the program.