I recommend reading w3 .
In many cases, you can remove the extension. Let's say if you need a link to a page, then I would recommend to remove, for example http://example.org/first/ .
But for the content I would recommend to leave. For example, if on the page http://example.org/first/ we have a video, then the link is better to do this http://example.org/first/coolVideo.mp4 , and not http://example.org/first/coolVideo .
The extension also allows the browser to understand what content is in front of it. For example, if you provide a link to an Excel document, for example, it is better to add the extension http://example.org/first/myExcel.xls . Then the browser when downloading will give a choice, than to open this document after the jump. Smart browsers can probably determine this, but not all.
Also, some recommend hiding extensions, as this complicates the hacking process.
If you use CDN, then the extension is also very useful.