What is required will depend on where you are showing. Some may require that you have your horse vaccinated for multiple diseases and others may not require any vaccinations at all. What you need to worry about is what is recommended by your vet for your situation to help protect your horse.
Core vaccinations that are recommended for all horses in the US by the American Association of Equine Practitioners are: EEE, WEE, WNV, Tetanus and Rabies. Beyond that there are vaccines that are recommended based upon risk. For any horse showing, you can bet that your vet is going to recommend at least 2 of these risk-based vaccines--Influenza and EHV. If there are any other risk-based vaccines that would be recommended and how often you should give them is going to depend on a few different factors, so you should discuss them with your vet.
So, talk to your vet about what vaccinations to give. And then check the rules of each show prior to attending so that you can ensure that you meet the requirements. I cannot imagine any show would require more or different vaccinations that your veterinarian would recommend.
Licensed Veterinary Technician