Jason Todd was the second Robin. Batman met Jason when Jason was trying to steal the wheels off the Batmobile. Jason's parents were killed in the same situation as Dick's, and Batman took him in. Batman had Jason fill in the role vacated by Dick. Jason, while chasing a woman he felt was his mother, was killed by the Joker. The decision to kill Jason off was made by a phone-in poll conducted by DC. Batman has a memorial to Jason in the Batcave, with his Robin costume and a plaque that reads, "Jason Todd - a Good Soldier."
Tim Drake is the third Robin. Tim discovered that Bruce Wayne was Batman, and after much prodding from Alfred, Dick, and Tim, Batman agreed that Tim should become Robin. Batman's stipulation was that Tim had to prepare for a very long time, to prevent him from meeting Jason's doom. Tim is the Robin in the current comics. Tim trained Jean Paul Valley in his role as Batman. Tim's parents were kidnapped by terrorists; his mother was killed and his father was left a near-vegetable. Tim is highly skilled in using a computer, and often does a lot of research for Batman on the computer.
The Dark Knight Returns offered a fourth Robin, Carrie Kelley. Carrie was a young teenager who was saved from a mugging by Batman, after he came back from retirement. Carrie made her own Robin costume, and let Batman know that she was interested. Batman accepted her help, and Carrie actually saved his life at one point in those chronicles.