This is the newest version of their architecture I've seen [0]. Compare to an overview from 2009 [1].
tl;dr StackOverflow's architecture is fairly simple and has done mostly vertical scaling (more powerful machines) and bare metal servers rather than virtual servers. They also realize their use patterns are read-heavy so there's a lot of caching and they take advantage of CDNs for static content which completely offloads that traffic off their main servers.