I received an email with an Mpp file attached. I can't open it. Do I need Microsoft projects to do so?

Yes, but you can use Project viewer: Microsoft Project Viewer - Free information (http://www.microsoftprojectviewer.com/)

I have to wonder about people that would send an attachment without first checking if the recipient has what's needed to open that attachment. I can understand sending a PDF, JPG, maybe even a DOC file since those are standards and the ability to read them is built into most PCs. But MS Project is not a standard app.

As Ben noted, MS does provide a viewer so you can see the contents of the file, just can't make any changes.