It’s Easy, Just Open Your PDF Viewer
Viewing an Adobe Illustrator File is as easy as opening your PDF viewer and then opening the file. The easiest way to do this is by first opening the PDF Viewer software and the folder with the .AI Illustrator file in it and then dragging your AI file into the screen area of the PDF Viewer.
I recommend using FoxitPDF Viewer which is available at the reputable website http://www.download.com -- PLEASE NOTE: When installing any software make sure you read every page of the installation and only install what is required for that software. Most free software online these days is packed with Adware or new browser software and being careful can avoid the dredded ask.com and other software installs you didn't intend to install.
This should be all you need to do. If you have any trouble then simple rename the file from .ai file to a .pdf file but this should not even be necessary!
Now you can easily see any Illustrator file without have Adobe Illustrator.