Ditch the runoff water?

Should I get rid of any runoff water?

You don't want your roots sitting in standing water, ever, but especially if your feeding with liquid fertilizer. Generally speaking you don't want standing water as it attracts all kinds of life, insect, bacterial, fungal.
I like to use draining tables so run off feeds in to an easy to remove container. Weather I dump that container or not depends on my seasonal conditions. Rh% is an important environmental factor, and run off is a free controlable variable. March-Octoberber I have to worry about bugs so standing water is a no go, also humidity is high during high temps so extra moisture is not helpful in anyway. It's dry in the cold months and I crank my light intensity up so letting my run off evaporate helps keep my rh up, I just sanitize my catch bucket every 3 or 4 water cycles

you can get away with water in the pot dishes, as long as you let it dry out in between watering/feeding's but its best not to let them sit in water as VaSmile stated

What else would you do with it?
I give it to my outdoor plants around my house.

If your in soil there shouldn't be much run off.