Pretty much everything we have runs on Oracle. We've been using them since the beginning of PayPal -- in fact, we only recently phased out one of the databases that traced its roots all the way back to Confinity. We figured out pretty early on that Oracle connections are expensive to open, so we actually wrote a thing called the Oracle Connection Cache (or OCC for short) -- it keeps a cache of open connections to our Oracle servers and speeds up DB queries quite a bit.
As far as NoSQL databases...I'm not aware of any that we use on our production systems. I think there might be some that we use for doing analytics on our back-end.