It is possible to open Microsoft Visio files in Ubuntu? Perhaps something like Dia, or OpenOffice Draw?
It is not an emergency, but it would be nice...
Quick update to the existing answers: the current version (4.3) of LibreOffice Draw opens .vsdx files indeed, although they appear a bit mangled so they'll require some work on it.
You could use an online service like http://www.freepdfconvert.com (there are dozens) to turn it into a PDF and with that view it or manhandle it in Inkscape, et al.
But as for direct opening, not yet, I'm afraid. It's fairly niche too so I wouldn't expect a solution any time soon.
Open diagrams.net and drag and drop the file into the editor (.vsdx only)
If privacy is an issue use the desktop version
I installed Visio in Ubuntu, but first I installed Wine. It's working fine (there are some issues!). I don't know if there is another way to open that kind of files. I tried with OpenOffice.org Drawing but nothing happen.
If you have access to Visio 2003 or higher, you could try to convert it to .SVG That format is easily readable by both Dia and Inkscape. If not, you're in a world of pain because raw Visio is not easily convertible.
Try the "Free Visio Viewer (Mac, Windows, Linux)" add-on in Chrome, by LucidChart. I just tried it in Ubuntu 14.04. It seems to work well.
As far as using LibreOffice goes, it's May 2018 and I'm using LibreOffice 6.0.1.1, and unfortunately LibreOffice Draw still won't open .vdx files as far as I can tell. :(