If you open the file with a text editor there is a good chance the version of Solidworks it was created with will be in the first couple of lines.

Thanks 3DDave!

CAD 2015

Your version of SolidWorks is older than the version used to save the file you are trying to open.
You can check the file saved version by using Notepad or other plain text editor and open the CAD file and check the header.
CAD files are not backward compatible!

"Wildfires are dangerous, hard to control, and economically catastrophic."

Ben Loosli

Thank you, Ben!

CAD 2015

Good grief guys. This has never been true for SolidWorks files. There used to be a numerical code buried in the file (not in the header) that you could use to look up which version the file was saved in. You could also find readable text strings such as all the custom properties and their names, feature names, etc... Now (since like 2015 or so), the content of SW files is compressed/encrypted such that there is zero content readable in a text editor.

Spot on handleman. The way to determine the version of a Solidworks file is to view it's properties in Windows Explorer.

Note that this only works for versions up to whatever you have installed. If you're running 2016 and you try to look at a 2018 file, it will only tell you "future version".