For most things you don't need the analog CD-audio connector. The only two cases in which I would suggest connecting it, would be if:
1) You want to listen to audio CDs as background music, while you do other things that use a lot of IDE or PCI bus bandwidth (heavy ripping/burning, video-capture, etc.)
2) You still boot to real-mode DOS to play older DOS video games. Most of them require the analog audio cable to play the background music off of the CD as normal CD audio.
The vast majority of people out there don't need it, and by connecting it, you also take the minor risk of coupling more noise into the analog audio subsystem of your PC.