There are two basic types, wood or metal, with a wide range of choices within those categories.
Wood Stands
Wooden hammock stands
They're available in a variety of woods, with cypress a popular choice. Oak is very dense, hard and sturdy but correspondingly expensive. Teak is a highly expensive option, but one that offers great beauty and long lasting support.
But wooden hammock stands have some drawbacks. As a natural product, even when processed and coated with modern techniques and materials, they will deteriorate. UV radiation, moisture and other natural environmental factors will cause wood to age and eventually rot. Though with proper coatings (re-applied as you would to your home) they can last years, their lifetime is shorter than metal hammock stands.
Metal Stands
Metal hammock stands offer long-lasting support and come in an array of designs.
Inexpensive aluminum or stainless steel stands are an option. Painted in an attractive color that complements your hammock and home design, they can be a lovely addition to the decor. But unpainted, they are prone to oxidation. If painted, they may eventually look old due to chipping or fading. Expect to exert some effort to care for them.
Regular care to keep your metal hammock stand
Whether selecting wood or metal, stability is fundamental. Any hammock stand worth buying should support at least 500lbs. Even if you weigh only 100lbs, you exert much more force when sitting down or getting back up again than you do simply lying still. Also, you never know when someone is going to want to join you on such a relaxing piece of furniture. You want a wide margin of error in any case.