There are lots of collective nouns, and some of them might be useful to know if you do the cryptic crossword; such as a murder of crows, so, by all means learn them if it interests you. In the meantime here are some you might actually use in day to day English.
Groups of people working together
Army: an organized military force equipped for fighting on land.
Cast: the actors in a certain movie or play.
Crew: all the working members on a ship or plane.
Family: a group of people usually related by blood.
Gang: an organized group of criminals.
Staff: the people who work in a company or place of work.
Team: a group of individuals playing on the same side generally with the same objectives.
Groups of people in general
Audience: spectators or listeners at a public event.
Crowd: a group of people, gathered together.
Mob: a large disorderly crowd.
Movement: a group of people with similar political/musical/social ideals.
Throng: a busy group of people or animals.
Groups of animals
Herd: a herd of cows, a herd of goats, a herd of deer
Flock: a flock of sheep, a flock of birds
Litter: a litter of kittens (usually of baby animals)
Pack: a pack of wolves, a pack of dogs
Shoal / School: a shoal of fish, a school of fish
Swarm: a swarm of bees (swarm is used for a group of flying insects)
Groups of things
Batch: a quantity or consignment of goods produced at one time - a batch of bread / a batch of letters.
Bunch: a number of things, typically of the same kind, growing or fastened together - a bunch of flowers / a bunch of grapes / a bunch of bananas.
Bundle: a collection of things or material tied or wrapped up together - a bundle of newspapers / a bundle of sticks.
Collection: a group of objects or works to be seen, studied, or kept together - a collection of stamps.
Fleet: a collection of ships or vehicles - a fleet of fishing boats / a fleet of taxis.
Pack: a small cardboard or paper container and the items contained within it - a pack of cards / a pack of cigarettes.
Heap / Pile / Stack: a quantity of objects stacked or thrown together - a pile of clothes / a heap of bodies / a stack of plates.
Set: a collection of things that belong together - a set of tools / a set of underwear / a set of compasses, a set of cutlery.
Stash: a group of hidden things - a stash of cash, a stash of beer, a stash of weapons.