Here are some popular types of straps to suit different occasions and uses:
NATO Straps
Rubber/Silicone Strap
The said strap is a good alternative for a sporty look that offers good flexibility and comfort. Although it is not very suitable for formal looks, it is good for everyday wear. Easy to clean, and does not leave perspiration marks unlike their leather or nylon counterparts.
Leather Strap
Mostly installed on pilot watches, leather is a great material which darkens and age with use. An elegant and classic look when paired with the right watch and provides good support on the wrist. Various versions of leather such as ostrich or crocodile leather are being used as well.
Metal Bracelet
The most commonly see would be the metal bracelet on watches, it is able to fit in for almost all occasions be it a casual or formal. The stainless steel variant are highly durable and wear well in all kinds of weather. Some kinds of bracelets also have mechanisms for minimal adjustment to its length to account for diving purposes or temperature changes (expanding and contracting of length).