It's hard to say objectively who's the greatest, but in my list Messner is at least in the top3, not in the least place as he is still alive!
But there are many climbers, both known and unknown who have climbed amazing things. How about Doug Scott or Herman Buhl? Or Heinrch Harrer and Lynn Hill? Jerzy Kukuczka maybe?
If you and others post some names to nominate here I will ccreate a poll so you can vote for it