What type of equipment is used for farming?

This depends on what farm you are talking about. Crop farms use tillage and crop equipment: Swathers, combine harvesters, plows, packer harrows, cultivators, discs, augers and tractors are mainly used on a crop farm.

Livestock farms that raise cattle use the same machinery as the crop farm, only they also have haying and silage equipment: forage harvesters, silage dump wagons, rakes, haybines or hay mowers, balers, etc. Manure spreaders are also found on these types of farms. Fencing equipment, handling facilities are also found on cattle operations.

Sheep and goat and hog operations also have handling facilities similar to cattle, only their designed to handle sheep/goats or hogs. Other equipment are pretty much the same as what is used to grow crops and hay to feed cattle and horses.