What reason(s) did you have for not leaving a tip at a restaurant or place of service?
If the service is very bad. I can think of very few occasions when I left either zero tip or an insulting tip.
Once was in a hotel with a restaurant attached. The waitress couldn't have been less interested. When our food came she literally dropped the plates on the table and had turned away by the time they landed. She got a dime as her tip. My wife didn't think she deserved that - I didn't either but didn't have a nickel.
Another time was in a place we go to reasonably often but the waiter we had one day was utterly disinterested in us. For some reason he was able to find lots of time for another table. That was the table with four college-aged girls sitting at it. We emailed the place to complain about him, and I think I left him a $2 tip on a $50 check. I was seriously tempted to write "keep it in your pants" or similar in the "tip" section of the bill.