I would like to maintain a list of objects that is distributed between N load balanced servers: whenever a client changes the list on one server, I would like these changes to migrate to the other servers. So, I guess this is a case of master-master replication.
What is the simplest way of handling this? One simplifying fact is that each change to an object in the list has an associated increasing version number attached to it. So, it is possible to resolve conflicts if an item was changed on two different servers, and these two deltas make their way to a third server. 

Edit: clarification: I am quite familiar with distributed key-value stores like Memcached and Redis. That is not the issue here; what I am interested in is a mechanism to resolve conflicts in a shared list: if server A changes an item in the list, and server B removes the item, for example, how to resolve the conflict programmatically.