It's bad enough when a customer stiffs you on a tip for a round or two, but what if a customer repeatedly stiffs you on every single round that they order? How I handle the situation all depends on the bar I am working at. Sometimes bars and restaurants have a strict policy about customer service. They fumble over themselves doing whatever it takes to make the customer happy. That means that when a customer doesn't tip, there isn't much you can do or say. You just have to accept it and hope that the next customer does tip.
Then there are places where providing good customer service isn't as much of a priority as it is to pour an accurate shot amount. When customer service in general goes by the wayside, you have a little bit more flexibility in how you handle the stiffers. I'm the type of bartender that feels it is important to always provide good customer service. My philosophy? The better the service, the better the tip. It also increases the chances of return business.
When some bartenders call out a customer right after the first or second round, I give the customer three chances (just like three strikes). After the third round of being stiffed, I pull the customer aside and check in with them. I ask them if the drinks and the service being provided is okay. If they answer yes with a smile, I then let them know that when a customer doesn't tip, it makes the bartender think that there is a problem with the drinks or service and because they haven't tipped me on any of the rounds that they've ordered, it leads me to believe that there might be a problem.
Now this conversation can go a few ways and you have to be prepared to deal with the repurcussions. Either the customer will "get it", apologize and grab whatever cash is in their pocket and leave it on the bar as a tip. Or the customer could just be a complete jerk who doesn't tip and just walks away. Then there are the customers who don't speak a lick of English and don't understand what you're saying so they just smile and walk away.
With the non-English speaking customers, I've had the best luck when they come in groups because there's always one person in the group who does speak English. The English speaking group member will see that a conversation is taking place at the bar, come up to the bar to make sure that everything is okay and when they realize what we're talking about, they'll leave some sort of tip.
Most importantly, as a bartender you have to pick and choose your battles. You don't want to be the whiny, rude bartender, but then again you work for tips and don't want to be constantly ran over by the cheap customers. In the big picture, the tips all even out at the end of the shift anyways. For the one person who doesn't tip, there will be someone who over tips. So don't get upset over the one person who stiffs you on a round. It happens. But when a customer does it each and every time they order a drink (even more so if their order is complicated and their high maintenance), then having the conversation might be a good idea.