My Bromptons all have mudguards, the superlight has titanium stays. I've toyed with taking the mudguards off that one but the word on the street is that they don't stand well when folded if you remove them. They delaminate after a few years and one of the back ones has a broken support.
MTB has them but they are broken so if I get a new back wheel for it I'll probably take them off. I had Dave Yates build it with eyelets for mudguards and a rear Blackburn. I didn't have the Bromptons back then. It doesn't need to pick up the utility miles anymore.
Racing bike doesn't have any and has no way to fit them without using clip on stays.
Trike has a front mudguard. There is no good way to fit rear ones and the wet stuff goes past your shoulders. It only hits you when cornering because you have to shift your weight to the inside of the curve. A friend had mudguards on the back of his and they were always getting broken.