The most common would be the classic Tri-Fold. it is mostly used for product pamphlets, take-out menus, promotional brochures, and many other applications. It can be easily inserted into envelopes, so it's a great option for mailing. A "Letterfold" is basically a portrait Tri-Fold. It has a different name because it is mostly used for letters and documents inserted into a #10 envelope.
A variation of the Tri-Fold is the Z-fold, where the last panel is folded outwards instead of being tucked in, forming a "Z" shape. Z-fold is mostly used for bilingual items, as each side of the folded brochure serves as a front cover panel.
Another popular fold is the half-fold, as it is...