What are the must-read search trees paper?
Sleator-Tarjan '85 and Demaine et al '09 definitely belong on any such list.
There is a lot of other recent work related to splay trees and dynamic optimality, for instance:


Applications of forbidden 0-1 matrices to search tree and path compression-based data structures, Seth Pettie, SODA 2010
An O (log log n)-competitive binary search tree with optimal worst-case access times, Bose et al, SWAT 2010
Upper bounds for maximally greedy binary search trees, Kyle Fox, WADS 2011.
De-amortizing binary search trees, Bose et al, ICALP 2012
Pattern-avoiding access in binary search trees, Chalermsook et al, FOCS 2015
Weighted dynamic finger in binary search trees, Iacono and Langerman, SODA 2016


On more classical lines, I think


Rank-balanced trees, Haeupler, Sen, and Tarjan, ACM TALG 2015


is worth including as an elegant unification of AVL and red-black trees.