Both my bikes have mudguards. Both have rear mudflaps too and one also has a front mudflap (the other has a front mudguard which ends quite near the ground).
On the utility-tourer in utility mode, they mean I can go shopping without appearing to have suffered an attack of diarrhea, and in touring mode they mean I can ride all day in comfort without abrading my arse. On the other bike, they mean the same things.
The only problems they cause is when they get clogged with mud. My ideal bike would have about 3cm of clearance between tyre tread and mudguard.