As a former WoW player, my experience was that the login server was always the weakest link in the chain.
The world servers were usually impressively stable, even handling exceptional load (e.g. new expansion pack releases) quite well.
But the login server(s) just never seemed to cope so well, and would frequently be down whilst the world servers were fine. (meaning that if you lose connection in a raid/dungeon, you can't get back in, but the other players are waiting for you!)
And now that the WoW login system is merged into Battle.Net, Starcraft 2 can become unavailable when WoW is under heavy load (as happened for a couple of hours when Cataclysm launched)
So if you're building a game that will have very large numbers of users, scalability and performance of the login system is very important, too.