Lots of copy/paste is usually a bad sign, but generally speaking each form you create is unique in several ways.
But essentially, yes you can include files much as you do with CSS files.
Look at the include and require functions.
Most developers use these methods a lot in especially to maximise the re-use of code.
Maybe you could post some examples of what you mean -- is it the form elements, PHP form validation or mysql storage that you suspect could benefit from less code duplication?