Check the date on this thread Newbie,
I'm up to 37 now....I think.
It never stops, but it does slow down and starts to evolve. You start to pass up decent finds that don't fit your needs or you can't pass along easily, and you get much more particular about quality.
I started my adventure on this,
A battered, bent unidentifiable wreck I dragged home for $20.
And now I mostly play with 531 and Vitus bikes, and a couple of vintage C-Dales. With the odd gas piper tossed in if it's historically interesting.
Overall I'm pretty well done, there are only three bikes on my "grail" list, and one of them is sitting in a friends garage in Michigan. So I'm down to watching for a Falcon Merckx and a white 70's PX-10.