By purpose and (approximately) by screen size:
Desktop replacement – emphasizes performance, is less portable, 15" and larger screen;
Standard laptop – balances portability and features, 13-15" screen;
Subnotebook – emphasizes portability, has fewer features, 13" or smaller screen.
Budget – a cheap, lower-performance standard-sized laptop;
Tablet PC – Has a touch-screen interface, may or may not have a keyboard;
Inner view of a Sony Vaio laptop