Moons

The moons in the Kingdom of Loathing, Ronald and Grimace, affect several things. There are certain days on which stat gains are higher for one particular stat, as is the HP or MP gained from resting, and the moons affect Temporary Lycanthropy (obtained from blood of the Wereseal), the Grue familiar and the Talisman of Baio's effects. Here's how it all pans out:

Ronald	Grimace	Stat Gains	Resting	Temporary Lycanthropy	Grue	Talisman of Baio
		Moxie		-100% Muscle	Attacks	No effect
				-75% Muscle	Attacks	+10% All stats
				-25% Muscle	Attacks	+30% All stats
				No effect	Attacks	+40% All stats
		Mysticality	x2 MP	+50% Muscle	Does not attack	+60% All stats
				+25% Muscle	Does not attack	+50% All stats
				+25% Muscle	Does not attack	+50% All stats
				No effect	Attacks	+40% All stats
		Muscle	x2 HP	No effect	Attacks	+40% All stats
		Muscle	x2 HP	+25% Muscle	Does not attack	+50% All stats
				+25% Muscle	Does not attack	+50% All stats
				+50% Muscle	Does not attack	+60% All stats
		Mysticality	x2 MP	+50% Muscle	Does not attack	+60% All stats
				+25% Muscle	Does not attack	+50% All stats
				-25% Muscle	Attacks	+30% All stats
		Moxie		-50% Muscle	Attacks	+20% All stats

For a rundown of upcoming moons see this moon page.