There is not one definative answer to this question. Often dentists and patients have more than one option when treating a loose tooth. The dentist should evaluate the degree of looseness, the remaining supporting bone and periodontal health of the supporting tissues, when making a treatment decision.
If the looseness is possibly the result of a poor periodontal condition of the gums supporting the tooth and sufficient supporting bone remains, then root planning and treatment for periodontal disease should be performed, before making a final decision about the tooth.
If the looseness is secondary to an abcess of endodontic origin, usually root canal therapy will help improve the situation. Endodontic abcesses can cause bone loss around the apex of a tooth and this area of bone loss can gradually fill back in with new bone if the root canal is succesful.
In some cases, when a tooth is made healthy, but still is displaying too much mobility, a dentist can connect it to an adjacent tooth or teeth(with connected crowns or a maryland splint), so that it is splinted and will experience less or no mobility.
Sometimes the looseness stems from not enough supporting bone being present and no amount of dental treatment will improve the situation. In this case having the tooth out is usually the best option. If the patient has sufficient remaining bone or can have bone grafting, then an implant can be a good option.