Do Ron Weasley and Hermione Granger kiss in Harry Potter the Half-Blood Prince?

No, Ron Weasley and Hermione Granger do not kiss in Harry Potter and the Half-Blood Prince.

They do share a dance at Slughorn's Christmas party, but they don't kiss. It's a significant moment because it marks the beginning of their growing feelings for each other, but they don't yet express them in a romantic way.