I like consistent hashing (https://en.m.wikipedia.org/wiki/Consistent_hashing). When a hash table (or load balancing pool) needs to be resized, it usually reduces the number of keys (clients) that need to be remapped.
In a similar vein, Maglev hashing has a more uniform distribution and decent reshuffling. I couldn't get my head around the explainaions that I had seen until I read this one:
It's quite a bit easier to implement and verify than consistent hashing, and carries the same benefits (minimal reshuffling on ring resizes, etc)