Broken, cracked, or extensively decayed teeth can be extraction candidates.
Some teeth will have extensive decay (dental caries) or else will have broken or cracked in such an extreme manner that an extraction might be considered the best, or at least a reasonable, solution. Of course there will be a number of factors that will come into play with any specific situation. In some cases the obstacles that present themselves might be so formidable that a repair for the tooth is simply not possible. In other cases the cost of needed dental treatment or else a questionable long-term outlook for the success of the treatment may be the reason an extraction is chosen.

Teeth that are unsuitable candidates for root canal treatment should be extracted.
Some teeth may require treatment of the nerve space that lies within them (root canal treatment) in order to make a repair. While most teeth typically are candidates for root canal treatment there can be complicating factors that remove this option. If this is the case and needed root canal treatment cannot be performed then the extraction of the tooth is indicated.

Teeth associated with advanced periodontal disease (gum disease) may need to be pulled.
By definition, teeth that have experienced the effects of advanced periodontal disease (gum disease) are teeth whose supporting bone has been damaged. In general, as periodontal disease worsens, a tooth is supported by less and less surrounding bone, often to the point where the tooth becomes loose. In those cases where significant bone damage has occurred and a tooth has become excessively mobile extraction of the tooth may be the only option.