I'm a fan of Robin. I can bet that a lot of Teen Titans fans do like Robin. But sometimes I don't really believe that he's a stable leader.
Robin has shown the audience that he's a smart, level-headed and serious leader. He's always able to get his team out of trouble, and as well to keep them in order and stop them from causing any trouble. He does his best to protect his team and truly cares for all of his teammates, and is always fighting for justice.
But he also puts his team in danger. He's obsessed with finding Slade and is willing to put anything, anyone in danger in order to defeat Slade. In the episode Haunted, he threatened Starfire, Raven, Beast Boy and Cyborg that he would destroy anything that comes in path of his way of defeating Slade, and he when he became Red X to learn Slade's secrets and defeat him, he attacked them, and nearly lost his friends trust- all for pretending to be a supervillain. Sometimes I believe that Robin puts fighting crime and defeating his enemies first instead of his friends, since he is always so stressed about defeating Slade or Dr. Chang and won't stop, even if his friends are in danger.
So, is Robin a great leader? Or an unstable boy who lives for defeating his enemies? We'll never know.