I actually count 32 on mine, but I have two headset spacers with 3 logos each.

Stem: 2
Spacers: 3 on each of 2 spacers = 6
Handlebar (apart from bar tape): 3
Headtube: 1
Cable pads (to prevent wear on headtube): 2 on each of 2 = 4
Fork: 2
Downtube: 2
Top tube: 2
Saddle: 3, including one low-contrast white on white
Saddle rails: 2
Seatpost: 1
Seatstays: 2
Hubs: 1 on each = 2

Most of these fall into the category of "fine print" however. The main visible logs are on the headtube, downtube, fork, and seatstays.