What are some types of aircraft?

Depends on what you mean. Aircraft is a nice noun that is both singular and plural. The usage isn't bad, it's clear when a craft of the moving type is meant, instead of of, say woodcraft, which was the one of the necessities for a working aircraft, or an aeroplane, or an airplane. It just follows the old rule of the Word "craft," either being the work itself or the result of that work, and old Words never work like the grammarians would like.

Some types of aircraft are aerostats, or lighter-than-air vehicles (balloons, blimps and zeppelins), fixed-wing aircraft (most of what you think of as airplanes), and rotorcraft; i.e. helicopters and autogyros, and also spacecraft that use wings to generate lift after re-entry, X-15, Space Shuttle, and Buran, for example.