Yes, you can copy your audio CD to hard disk with Nero. Select "Recorder"->"Save Track...", choose the drive in which your CD is inserted, select the tracks you want to copy, the format in which you want to save them, where you want to save them, etc., then hit "Go".
Nero can also save the contents of your audio CD to hard disk as an image file if you choose image recorder as your output device when "burning" an audio CD compilation. This way probably isn't what you are thinking about, since it saves in a format that isn't directly accessible by other programs.
Other popular programs for ripping audio CDs and making compilations are Exact Audio Copy and Feruio:
Yet another program that can rip audio is ISO Buster:
It is a general purpose ISO image manipulation program, so it doesn't have all the bells and whistles of the other programs mentioned above. It is easy to use though if you aren't a rabid audiophile.