The penny tip is a way to let the server know the service was deplorable. Not leaving a tip at all, is a way to get your point across, but the server might also take it as "they must have forgot" or "they don't tip".
Only two times have I not left a tip. Once at a place I used to go to a lot. My wife was working and a friend of mine and my son went to eat, and we were seated. The waitress took our drink order and I ordered wings and tried to order the rest of the meal too, but she said "I'll put the order in" and left.
Ok-no problem, but she never came back, and we waited and waited......
Finally the Wings came. I was not happy, and she said "Was there anything else?"
I said "Yes, our dinner order!!!"
She thought that was all we wanted. By now, my son is upset because he wants to eat, he was so little then, I always ordered for him right away so he could get his food as quick as possible, we eventually got our food, but she never checked on us, we had to ask someone else for refills AND for the bill. Sorry, no tip for her.
The other time, My wife laid down the law.
Went to a pizza place, ordered a pizza with breadsticks. Breadsticks never came, we got the pizza and I politely asked what happened with the breadsticks. She just told me we didn't order them. I said, Yes, I was sure we did. She apologized and said she must not have heard, I said no problem, but my wife was mad because I guess the waitress had told me "I'll be right back with your sticks". Hell, I had forgotten too, that I heard that! Anyways, no tip for her either. I felt bad, but Mom is the boss!