How can I increase Skyrim's Volume?

If you're on windows 7 (I think Vista as well?), try the following:

1. While Skyrim is running, alt-tab back to your desktop.
2. Click the volume icon in the system tray, then click "mixer".
3. In there, there are separate settings for each application currently running.
4. Move Skyrim's slider higher, and it should raise the volume relative to your other applications

Likely your volume on the mixer is already at max, so the best way to do this is go to 'playback devices', click the one you're using, head to enhancements and turn on 'loudness equalization'.

Was having the same problem but this fixed it instantly.

Loudness Equalization is bad, as it negatively affect the full experience of the audio by limiting the range. Now probably if you're using a laptop or some cheap speakers it won't make much difference but otherwise another solution is preferable.

There is another solution here.

(...) if you have Realtek onboard sound and are using stereo speakers or headphones, switch the speaker configuration to 5.1 and uncheck the center channel / sub / rear speaker options.

This worked for me.

The reason, according to that forum post, is because The game was designed to support 2.1, 5.1, and 7.1 sound.