Guiding

The first reason to connect a computer to the mount, unless you have a dedicated astrophotography camera that need control software, is guiding.

An almost sacred method is phd2 guiding. It's used by almost everyone, although there are others, the better versions come at a hefty price. Phd2 is freeeee and with so many users that support is readily available. There are versions for Window, Mac and linux. 

Windows or Mac?

Windows....*sigh*

The most common hardware is a window PC. The reason for this is the ASCOM initiative. 

This is a standard for communication which allows one computer to talk to anything that is ASCOM compatible. Very nice indeed. But it only work on PC. #€&£$∞@! There are talk of some platform independent version, but it's not here yet.

Mac or Linux?

For us Mac or linux users there is indi. This is pretty much the same thing as ASCOM and through KStars MacOS release we have a nice planetarium app with the ability to connect pretty much anything and get it to work together. 

Linux users have indi server and can use PHD2 and other hardware that way. KStars is also available for linux. 

Till this day I'm on team Mac and Linux. And I think it's been working ok so far. Maybe I'm just stubborn and should just do like almost everyone else.