Since this thread has morphed a bit from its original intent (choosing just one grease), I figure we can add a bit to it.
Just one grease, bearings, light medium duty on pins, you keep up with your greasing, prefer less staining? Amsoil Synthetic Multi-Purpose #2.
OK with having a different grease for bearings, don't mind black stains, beat the crap out of your pins, work under harsh conditions, sometimes slack off on your greasing? 5% moly grease. In order of preference, TRC Paragon 3000, TRC Chassis 880, Schaefer 238, CAT branded 5% moly. I'm sure there are others here. 5% moly is important, but so is base stock.
Grease high speed bearings only, or don't mind having a special grease for that? Amsoil Dominator Synthetic Racing Grease.
I welcome alternate suggestions, that have spec sheets showing better performance for these use cases.