Yes, people still wear dentures:

Dentures are custom-made, false or fake teeth that replace a few or all of an individual’s original teeth. They are designed to fit comfortably over the gums to substitute missing teeth. They can also be used to close gaps between teeth as a preventative measure for possible dental problems later. Complete dentures are removable and partial dentures are normally fixed or permanent.
There are different kinds of dentures, made from different materials that vary slightly. Modern dentures are mostly made with ceramic, acrylic resin (a versatile type of plastic) and metal. Generally the structural base of partial dentures is made of metal, covered with plastic. The clasps that attach these dentures to existing teeth are also made of metal. Porcelain dentures used to be very popular and are still used today to a lesser extent, but for the most part they are made from acrylic these days due to the fact that they resist impact better than porcelain, are more easily replaced and more durable.

Who are dentures best suited for?
Dentures are most commonly suggested by dentists to adults who have lost teeth due to issues like tooth decay, gum disease or tooth problems caused by genetic defects, trauma to the teeth, the use of drugs or severe malnutrition. Generally adults wear dentures but there are a few instances where your dentist might suggest partial, temporary dentures for a child. This might for instance happen if the child lost baby teeth too soon (e.g. in the case of a fall where a tooth or teeth got knocked out and a denture will keep the space for the missing tooth or teeth open). If the child’s front teeth or a tooth in the front was impacted, a temporary tooth might also be suggested. Genetic defects or massive tooth decay could also result in a child having to wear dentures.

If you have lost all your teeth or have had to have all of them removed for whatever reason, dentures will enable you to regain abilities like eating comfortably, sharing big smiles, boost your self-confidence and self-esteem, provide you with possibly better career options and improve your overall health.

If you only require partial dentures, they will replace the few teeth that are missing, prevent crooked or tilted teeth caused by gaps, help you to bite and eat more easily, speak more clearly and boost your self-confidence, self-esteem and overall health.