I'm assuming a Windows PC, here.
If your new PC and old PC are not too different, you could try cloning your old hard disk and putting it in the new PC, then running a windows repair and installing the new drivers.
Specifically, I think you would have to move to the same type of processor (intel-intel or AMD - AMD), the same type of HDD (IDE - IDE or SATA-SATA), and the same graphics card (e.g. nVidia - nVidia), and preferably the same chipset for the clone to be successful.
Basically, if you can get Windows to load at all, even in safe mode, you should be able to install the correct drivers for the new hardware.
You would need to know what you were about to tackle it, though. And having a spare hard disk to test the cloning with would be a good idea.
If you have (or can get) a hard disk equal to or larger than your existing, and can get hold of Ghost or Acronis (or similar) to clone an image and you have the original Windows installation media and you have downloaded all the drivers for the new PC and put them onto a CD, it is probably worth a try.
At worst you will have made a backup of your existing HDD, and at best you will have transferred all your apps and music (relatively) painlessly.
BTW, I have successfully transferred images to non-identical PCs, but they do need to be pretty similar for it to work.
Oh yes - you may need to re-register Windows.
SD