(1) Microsoft’s Trident is used in Internet Explorer for Windows. It’s important because it dominates general web browsing, and because nearly all Windows applications use it to render web content. (What about the excellent Tasman, used in IE/Mac? I’d put it in fourth place, and consider it optional.)
(3) Gecko is used in AOL’s Netscape web browser. It’s important because Gecko is the second most popular rendering engine for general web browsing (albeit far, far behind Trident), and will be the most popular browser for AOL users.