The battleship (abbreviated BS) is one of the most common type of ship for fleet combat because their combined strength is staggering and seeing a fleet of these giants will turn your legs to jelly.
Trying to make smaller ships more attractive to pilots has been a goal of EVE developers for some times, however, many battleship pilots feel like their ships are losing their appeal since they are more and more at the mercy of smaller ships. Many tools which battleships use to fight these smaller targets (including small remote controlled drones) are becoming less effective.
Currently the use of a heavy nosferatu (or heavy NOS) is popular amongst battleship pilots, since this weapon drains any frigate's energy stores which allows battleships to fight them more effectively.
As for battleship to battleship combat, the use of Large caliber weapons is used. This includes large Railguns, Blasters, Lasers, Artillery, Autocannon, Cruise Missiles, and Torpedoes.