Renewal sent in by ordinary mail: 3 weeks
I sent my renewal application in with my old US passport (not due to expire for another 11 months) on December 9, 2016. The new passport was in my mailbox on December 29, 2016.
As another information point, I mailed everything in using the ordinary mail -- over 2 ounces, so it cost 89 cents in postage. No tracking, no expedited handling. I knew things were working out fine when my check cleared just before Christmas.