The most common fold for a Brochure would be the classic Tri-Fold. This will be familiar from take-out menus, product pamphlets, promotional brochures at information centers, and many other applications. It is ideal for mailing and can easily be inserted into envelopes.
A "Letterfold" is just a portrait Tri-Fold but has a different name because it is mostly used for letters and documents inserted into a #10 envelope.
A frequent variation of the Tri-Fold is the Z-fold, where instead of the last panel being tucked into the brochure, it is folded outwards, forming a "Z" shape. Z-fold is usually chosen for bilingual items, as each side of the brochure can be a different language. When it is folded, you will see, for example, French on one side and English on the other.
The second most popular fold would be the half-fold, as it is simple, easy, and economical. It is not as popular as the Tri-Fold because it only allows 4 panels in which to arrange content, rather than the 6 of a Tri- or Z-Fold. It is frequently used for newsletters, product handouts, and small maps or guides. It can also be used for inserts into catalogs, coupon flyers, or menus. Because there is only one fold, thicker stocks can be used, and additional finishes like lamination can be added without affecting the fold's functionality.