I own 17.
3 are being given away.
But I love collecting putters - so I'll bet I'm over 20 in few years.
I mostly play 2, occasionally playing a few others.
I have 10 (4 Scotty's, 5 Odyssey, and 1 Toulon) and one on the way. This year I am attempting to keep the changes in this spot very limited. In the last 6 months I have kept it down to between 3 (Toulon and 2 RSX). I think the battle will be between the Toulon San Diego and the 1W I have on the way.
I currently own six but have one main putter and one or two others that I'll occasionally rotate in this year. I have a Scotty that needs to go up for sale to thin the heard a little.