Two ways to amp up headphone listening
Provide better power to your headphones
First, a little background. Most headphones can generally accept a stronger output signal than that sent by a computer, or even an MP3 player or smart phone. This is especially true for over-the-ear headphones, which usually have a higher impedance than earbuds.
An external headphone amplifier can provide that additional power your headphones need for optimal operation. Plus, the signal from a good headphone amp is usually cleaner, to so you'll hear an improved sound even through a set of lowly earbuds.
Use a DAC with a headphone amp built in
Some digital-to-analog converters, or DACs, that are designed for computer speakers will also feature a headphone amplifier. For example, the Icon HDP from NuForce lets you bypass the DAC in your computer (so you can take advantage of the NuForce's better processing). Then, you can choose to hook up computer speakers when you want to listen loud and then switch to headphones later at night.
Whichever way you go, providing separate power for your headphones will give you better sound and perhaps more appreciation for tunes that were already on your computer.
Still more computer music options
If you can use speakers with your computer, don't use the speakers that came with your computer! My post How to get better sound from the music on your computer has some suggestions. And if you're looking for ways to personalize the music you listen to, read Three Internet music services worth checking out.