I don't want to say spam is a solved problem, but at least with gmail, I haven't seen anything spam-like hit my inbox in at least a month.
Gmail as replacement of FB is a little troublesome solution, I think. Gmail also has his privacy problems, though absolutely not as huge as Facebooks. I think, own (challenging) or paid Mail-providers should be preferred if you really want more privacy. Paid Mail-providers should be able to do the spam-filtering for you.