A missing tooth that is not replaced after extraction can lead to a series of problems 1) Migration of adjacent teeth and teeth in the opposing arch- causes disturbances in bite. 2) Such bite discrepancies can lead to natural compensations which in the long run harms your jaw muscles and the temporomandibular joint which causes severe pain in joint region or unexplained headaches! 3) The contacts that open up between adjacent teeth cause decay between them and would require extensive treatment 4) Teeth migration can cause ugly gaps in between teeth giving you an unpleasant smile.
All these can be prevented by replacing your extracted tooth within a month of extraction!
Prevention is Better than Cure