You might! But you also might not.
Below is the spreadsheet, directly from Common App, that indicates exactly what additional documents you will need to accompany your application to a particular school. If you have a letter from a teacher in the Common App, but you do not want to send it to all of your colleges, you can specify that on your application.
You can click the diagonal arrow in the upper right-hand corner of the document below to open it in a new tab.
As always, if you have questions, please see your school counselor:
Devine: A-F, Premo: G-Le, Lemke: Li-Ri, Fink: Ro-Z.