Never been a fan of Carrie Kelly.
Didn't like seeing Stephanie in the role either....she was always better suited as Spoiler and a foil for Tim. I guess that's why she was "made" Robin, to get him to want to come back.
My list is:
1.) Tim Drake
2.) Dick Grayson
3.) Jason Todd
4.) Damian Wayne
Tim has been the best character, especially when we talk about "in continuity" stories. He has been a tremendous detective, solid fighter and just a really great character. His personality and humor is all very likable and he has been there for some of Batman's best stories in the last 20 years. Off the top of the head: A Lonely Place of Dying, Hush, Legacy, Cataclysm, Fugitive, Knightfall, RIP, Under the Hood, Contagion, Face the Face, Unmasked!, War Games, As the Crow Flies, and Battle For the Cowl.
Dick has been around the longest, but as Robin, only has a few great story arcs to call his own in continuity. He is the original, and in skill--the best. His best stories include: Dark Victory, Robin: Year One, The Gauntlet, and Fortunate Son. However, he was a proven hero and great character in the original Teen Titans and in the 40 plus years of out of continuity stories.
Jason, while not the most likable character may have left the largest impression on Bruce's life. As the only Robin who was killed, he surpassed Harvey Dent as Bruce's greatest failure and was as much a casualty in his war as his parents were. He affected the entire Batman universe. Personally, I think his worth as a character was far greater dead than it has been since his resurrection, but...who am I to know? His best stories, well--were few and far. His best story by far was A Death in the Family but he was also good in Batman: Year Three the story that showed him being taken in, as well as background to Dick Grayson's time as Robin through some flashbacks. His best story as a "living/not being killed" character was probably, Batman: The Cult.
Damien has had only months to have the role so I cannot compare him to much.
The same can be said for Stephanie, who was only Robin for a handful of issues, in a known ploy to get Tim Drake back in the red and green tights.
Carrie Kelly, she was only Robin for one story--hardly anything to compare her to the "big three" who are legends in the comic book world for years.
For me it's: Tim out in first, followed closely by Dick, then a little further back is Jason.
-R