There are many ships that you can pilot in Eve Online. There are 4 main races that you can play and each race has their own ships that you can pilot in each class. So for example there are frigates for each race to pilot. You can pilot any races ships as long as you have the required skills.

There are frigates, which are smaller faster moving ships. Then there are cruiser class ships which are a bit bigger and are good for destroying frigates. There are battle cruisers, which are designed to destroy cruisers. Then battle ships, which are good for fighting bigger ships.

There are industrial ships for hauling cargo around space. Even bigger than industrial ships are the freighters. These are super huge ships and are very slow, but can haul a large amount of cargo.

There are covert ops ships that are designed to be able to cloak and sneak around space. Electronic warfare ships to assist the individuals who are doing the damage. Shuttles for getting around fast. As well as titan class ships that are basically locked out of high security space.

There are many more types of ships that you can eventually pilot in eve online, this is just a sample. Feel free to leave other ships and details that I might of missed in the comments! Online Game Forum is a great place to discuss online games.