In the context of hosting/cloud network what would probably be load balancer / reverse proxy which has the most state/sessions. And incidentally, LBs are probably the piece of dedicated network iron most ripe to be replaced with a bunch of commodity servers and some software.

Regardless, statefulness is bad of course, and less of it you have, the better you are off - we've seen this time and again: share nothing arch[1], Amdahl's law[2], locks-vs-RCU[3], memorizing tcp flows-vs-IP header hash[4,5], etc... Being able to make decision on current packet/memory access here and now, independently, without having to keep track of other flows/connections/sessions/threads beats alternative approaches every time [6].

[1] https://en.wikipedia.org/wiki/Shared_nothing_architecture

[2] https://en.wikipedia.org/wiki/Amdahl's_law

[3] http://www.rdrop.com/users/paulmck/RCU/hart_ipdps06.pdf

[4] https://tools.ietf.org/html/rfc2992

[5] http://www.juniper.net/techpubs/en_US/junos13.2/topics/conce...

[6] Intel's heroic effort to maintain cache coherency at all cost is a notable exception, although opinions vary wildly on whether this is actually the best thing to do, and how long they will be able to sustain it.