There are tables of pKa (the acid disassociation constant) available for a number of basic molecules and common functional groups. Evans from Harvard has a pretty good table online as a PDF. Interestingly, quite a lot of functional groups only have a DMSO pKa, which are always higher (in other words, less acidic) than in water.
Cationic species that deprotonate to form a neutral species often have a lower pKa in DMSO than in water. E.g protonated amines.
I spent way too much time with those tables back in my lab days.