Car Mode suddenly appeared - why? And how do I get rid of it?
It is included with Cyanogenmod and is based on similar modes in other ROMs. It is meant to provide you with what you need, but not so much as to distract you while driving. 

I do not know what is launching it, or how it is doing so automatically, but there may be ways to stop it:

Stop it in it's tracks

If you would like to remove it completely and not use it at all, install Titanium Backup, choose the Backup and Restore tab, find and select Car Home (I have version 2.2.1.2) and select either Freeze or Uninstall. 

Note: Freeze will stop the app from running at all, but keep it on your phone. Uninstall will completely remove it.

Double note: if you choose Uninstall, you may want to make a Backup there with the app first, just in case removing it causes unwanted side-effects.



Other, less intense options


In car mode, click the Right Arrow and choose Settings. From here, make sure that it's not automatically launching when connected to some bluetooth device, and try Reset to defaults, just to make sure nothing else is helping it along.
From the home screen, go to Settings -&gt; Applications -&gt; Manage Applications, choose the All tab, and find Car Home. Here, click the Clear data button.