This is a question that has come up sometimes in the Financial Aid office. Like everything else in the world of financial aid, the answer is simply "that depends". It depends on a few different things, but to help you think about the answer, here's what happens when you enter a school code on the FAFSA.
By entering a school code on the FAFSA, you are literally authorizing that school to be able to access your FAFSA information. It's a simple and easy way of sending your FAFSA information to a college that you are considering without having to complete the form again or bring/send copies of your FAFSA information to the school. When you enter the school code, then your information will become accessible to that school shortly (sometimes a day, sometimes a couple days).
This is especially helpful for students who are undecided about which school they should attend. If you are considering multiple schools, then there's no harm in entering the school codes for all the schools you are considering. By entering all those codes, you will make it easier for you to ask questions about your possible financial aid package for that school.
You are allowed up to ten school codes when you first complete a FAFSA, which means you can send your information to up to ten different schools. If you are shopping schools, then it's a good idea for you. Keep in mind that the schools you send your information to can also see the other schools you've sent your information to. If you've forgotten to add a school code that you wanted to, once your SAR had been produced, you can go back to the FAFSA website to add more school codes.
There's no harm in sending your FAFSA information to multiple schools, so if you're shopping for the best options, then send away!