I just got an email from Davis on Friday saying I’ve been denied admission to the school. This is pretty devastating because Davis was my dream school, and I had been so excited to attend 
has anyone else been rejected and is going to appeal, or has anyone appealed to Davis before? What are the chances of being accepted after an appeal?
Check this thread; http://talk.collegeconfidential.com/university-california-davis/1869745-how-do-you-appeal.html
Your chances will be dependent upon what new compelling information you submit to reverse the decision. There are many waitlisters that would get priority so make sure you have good documentation to support your appeal.
Before you spend time on a letter, you should honestly evaluate your academic achievements and be sure that they are squarely within or above the college’s averages. And it would help if you had some new compelling information as well. They will not change an admission decision simply because it it your “dream school”. If you write a letter of appeal that is your choice, but in the meantime I suggest that you look at the schools you did get into and find the best one for you.