Are there any long-term consequences of removing the appendix?

No. Appendectomy is one of the most common operations performed due to the high incidence of acute appendicitis. We believe that the appendix has a minor role in immune function, most likely in infancy. The long-term consequences of appendectomy are related to scar tissue that may have arisen from the appendicitis and/or surgery, which can rarely cause bowel obstructions or infertility.
No. This is a unnecessary body part and some states require its removal if you have an abdominal operation for other reasons.