If I'm sitting, I sometimes play the "how long can the ash get?" game.
If it's a cigar I haven't had before, I like to see some ash because it tells a lot about how well the cigar is rolled. It's just a matter of appreciation. I enjoy seeing that uniform, perfect ash.
But as a rule, I knock my ash off regularly. It's usually because I'm busy and don't want ash falling in whatever I'm working on.
I don't notice a difference in flavor, but I know for fact that my ashlessness causes goofy burns. My cigars run a lot and need touched up a lot. I also smoke really fast and that just compounds the issue.
I usually don't even notice how screwed up my cigar is until i have a burn that's run an inch down one side and it starts tasting funny. I'll try to correct it with the lighter, or I'll just grab some pruning shears, prune it back, and fire up again. :tu