Vecchi
The word vecchi literally means "old men." In fact they are usually the authority figures in the story -- "The Man" who is holding back the little people -- with the parts most typically fulfilled by the Doctor and Pantalone, although other characters like the Captain and Ruffiana can fall into this position as well. Storywise their usual purpose is to act as the villains and opponents.
In general the vecchi are portrayed as selfish, and quite prone to committing any and all of the seven deadly sins (lust, sloth, greed, pride, wrath, gluttony, envy.) They also are often hypocrites, demanding acts of sacrifice and loyalty from others they would never perform themselves, save for an occasional and usually sudden change of heart in the final act to allow a happy ending. They are almost always in a position of power over other characters, sometimes through their social position, other times by mere familial relation, but whatever it is -- they have the power to make their unreasonable demands of the other characters, and only clever schemes or incredible luck can get the victims out from under the control of the vecchio. Luckily, tradition dictates the vecchio is indeed almost always thwarted in the end.
It's of note that when a vecchio is defeated, he is almost never punished for his misdeeds beyond the embarrassment and disappointment of his failure. Many stories even see him given a consolation prize -- in Barber of Seville, Doctor Bartholo gets to keep Rosine's dowry as a peace offering even though she has broken her engagement to him. This likely has to do with deference to the vecchio's social status -- even if they are hated figures and the butts of ridicule, they are considered to be important and powerful people who are due a certain amount of respect, no matter how badly they've behaved. (There also may be a desire to end with a sense that no one will emerge from the happy ending still holding a vendetta.)
As characters, the vecchi are not traditionally played as sympathetic or emotionally complex, though some more modern productions do attempt to humanize them in this way. J.M. Barrie's Victorian-era play Pantaloon is an excellent example, in which Pantalone (Pantaloon) is not portrayed as a greedy, heartless old man but rather as a sympathetic gentleman who is past his prime, longing to recapture a hint of his former glory. Typically, however, the slapstick nature of the commedia requires they be played more one-dimensionally; it's not amusing when Pantalone falls and breaks his hip unless he's a jerk who deserves it.
Occasionally the vecchi are not of major importance in a plot, particularly in stories of the 18th century onward where the zanni might be the leads. In these cases, the vecchi are just treated as other zanni, with their comical traits enhanced.