The best caption for Sam Vimes would probably be "
Dirty Harry gone to seed". He is cynical, stubborn, rude and with an almost
religious contempt for authority. He is also a closet idealist (albeit a
disillusioned one) and a reluctant
diplomat and
nobleman.
Vimes' relationship with Vetinari is completely symbiotic - the conflict between them is what move the plots of the books as well as in-story events forward. Scenes of the classic "give me your badge and your gun" "you're suspended" and "I quit!" are written into almost every book.
Vimes is very much the gruff-but-decent copper, whose faults are really virtues that make him better at his job. Thus the reader is expected to fall in love with him despite the fact that, for eample, he never finishes a meal with his wife or goes anywhere without starting a riot in pursuit of a petty thief. Much supposed hilarity is derived from the he's-under-her-thumb-really school of comedy. I have never liked this aspect of the Ankh-Morpork City Guard series, and find it mildly annoying and not remotely amusing. Vimes himself, though a well written character, I find difficult to relate to in view of the fact that he's a total bastard.