I rinse through the line when I change a keg, using the PBW soultion I clean the keg with. This also cleans through the beer out dip tube as I simply connect the keg with cleaner in and run it through, then flush with clean water. I'm cleaning the keg anyway so flushing it through the line is no extra work.
In between sessions I cover the tap spout (think I got the covers from Malt Miller) and next time I run off about a 1/4 pint as this is warm and gets frothy until the 'new' beer comes through. I have only noticed the beer in the line going off if I haven't used the tap for a week or so (not often then) but the fresh beer was still fine.