Is there a program like Microsoft Visio for Mac?

Edraw Max is the Visio alternative for mac OSX. It has the Windows and Linux version too.

Most responses are commenting on flowcharts. Any opinions on how any of these apps (Lucidchart, Edraw Max, Libre Office, Omnigraffle) are for things like network drawings? Thanks in advance.

If you don't like online application, I will recommend you Edraw Max for Mac. It's rather easy to use, and can import/export visio files.

Don't rule out the free LibreOffice Suite which supports all versions of Visio from version 1 to present. It will open the Visio drawing in its Draw program, from which you can add to the original drawing, and save as an ODG drawing document. You can also export the Visio drawing in other graphic formats, or PDF.

Other recommendations here may better suit your needs.

Here is an Office 2007 Visio drawing dated from Fall 2009 opened in the current (as of this post) LibreOffice v5.3.1.2.

I have used Visio for doing 2D Top View Scaled Room Layouts. Would any of the recommended applications here be good for this use?

I think Lucidchart should meet your needs. It has most of the functionality of Visio, and is much easier to use. It runs in the browser, so it works on any operating system.

What did you use Visio for?

<I may receive some form of compensation, financial or otherwise, from my recommendation or link.>

Maybe you could tell us what it is. I certainly don't know what Visio is.

For some suggestions, read http://machow2.com/best-alternatives-visio-mac/

I haven't used Lucidchart specifically for business process mapping, but it's general flowcharting capabilities are great, so I imagine you will have a good experience. You can always try it out with their free trial.