There are two basic types of rig depending on the shape and way of attaching: square rig (most often square in shape) and fore-and-aft rig (triangular).
Square sails are those whose heads are attached to yards, and fore-and-aft sails hang along the keel line so that their foremost edge is windward. The most common fore-and-aft rig: Bermuda rig, gaff rig, staysail rig, lug rig and sprit rig.  

Depending on the type and number of masts, the following basic types of rigging may be distinguished:

Sloop – a single-masted sailboat with two fore-and-aft sails, one of which is spread on the mast, and the other one on the stay.

Cutter – a single-masted sailboat with one sail spread on the mast and one or more staysails.

Ketch – a two-masted boat with fore-and-aft rig; the after mast is a little shorter than the foremast, and placed before the rear edge of the designed waterline.

Schooner – a sailing ship with two or more masts and fore-and-aft rig, usually gaff rig or Bermuda rig; a topsail schooner – with an additional square sail.

Yawl – a two-masted boat with fore-and-aft sails; the after mast is much shorter than the foremast and it is placed on the stern beyond the rear edge of the designed waterline.

Brigantine – a two-masted ship, the foremast with square sails, the after mast with fore-and-aft sails.

Brig – a two-masted ship with square rig.

Barkquentine – a sailing ship with three or more masts; the foremast square-rigged, the others fore-and-aft rigged.

Barque – a sailing ship with three or more masts; the after mast fore-and-aft rigged, the others square rigged.

Full-rigged ship – a sailing ship with three or more masts, square-rigged.

In 2004, the STI, the organiser of the races, introduced a new system of vessel classification:

Class A: full-rigged ships with LOA of more than 40 m;
Class B: traditionally-rigged sailing ships with LOA of less than 40 m;
Class C: modern yachts with LOA less than 40 m, sailing without a spinnaker;
Class D: modern yachts with LOA of less than 40 m, sailing with a spinnaker.