How do I know if I need a crown on one of my molars?

Alternative. Your dentist can give you an opinion. With the development of strong porcelains, crowns can almost always be avoided today. Ask about porcelain onlays as an alternative to crowns. Not only are they more attractive, they also leave more of you own tooth. They can be made chairside in a single visit with the use of a computerized process called cerec.
Evaluation. Often times a dentist can tell you if a crown is needed as there are a myriad of reasons for needing a crown. Large restorations, fractures, replacing old crowns, or after root canals are just a few of the reasons for a crown. Speak to your doctor to determine why and make sure you ask why so you understand.
Basic logic. This is dependent on what percentage of the tooth is broken or unsupported, and also how healthy the remaining tooth structure is. Your dentist can examine the tooth and give you the best course or action... Crown, inlay, filling, extraction or no treatment at all.
Go see a DDS. If they can still salvage the tooth, do the crown. Otherwise later you will need the tooth implant which is more expensiv e.