The consequences of not getting a dental crown depend a lot on why your dentist thinks you need a crown. If you are getting a crown to protect a badly decayed tooth, then not getting a crown will probably lead to more decay, meaning a bigger cavity than you already have. Untreated tooth decay puts you at risk for tooth pain, a cracked tooth, sensitivity of the tooth to hot or cold temperatures, and a serious type of infection called a tooth abscess. Eventually, a decayed tooth will fall out completely or will need to be removed by your dentist.
If you are getting a crown to keep a cracked tooth together, the crack or fracture could become worse if you don't get the crown. Fractures in the teeth can lead to tooth decay or even infection in the innermost part of the tooth, because bacteria can leak into the crack and infect the tooth.
If you are getting a crown for cosmetic reasons (for a stained tooth or badly shaped tooth that makes you feel self-conscious or embarrassed), choosing to not get a crown just means that your tooth will have the same appearance.
If you are nervous about getting a dental crown placed, talk with your dentist. Having a conversation with him or her could go a long way toward making you feel more comfortable with this procedure.