Check out our new poll about PCB thickness.
Think as in flexible thin? Or as in 1/32", 1/64"?
Personally the reason I make boards for my circuits is because they need to fit into very small spaces, usually inside models or other pre-existing objects. Making the boards thinner isn’t critically important to me but it would be very nice.
I think thinner boards might be useful when you are making something small (and don’t need the immense strength of a 1/16" board) or need it to be lightweight, like for use in a UAV.
Thinner boards would be good for designs with RF antennas/microstrips (2.4Ghz) as the impedance would be easier to keep @ 50ohm with bottom side ground plane. With the current 0.064" FR4 boards, traces have to be around 120 mills for 50Ohm. If the board thickness drops to 0.032", the RF trace can shrink to 60mil.
I rarely use thinner boards, they flex more and SMT parts can crack easier. Although it sounds good for small slim projects.
Thicker boards FR4 0.125" 1/8" thick I use for heavier parts (i.e. transformers, big capacitors) and gear with SMT that’s going to get thrashed a lot like wireless microphones.