I have Version 2.8.2 running fine on a recent iMac running Yosemitee. I have tried the install of 2.10.1 from http://www.kyngchaos.com/software/qgis but it doesn't work. I would like to be able to install both versions so I have 2.8.2 as a backup while I try and get 2.10 running I know it is easy to run two versions on a PC if you are having issues but I can't see a way to do this on OSX
Note: I'm on Yosemite and I've tested the below for only about a week.
I have success creating a folder within my Applications folder called something like QGIS_28, as QGIS 2.8 is my currently installed version. I drag the already installed QGIS 2.8 app into that folder, then proceed with installing QGIS 2.10. I can also create an appropriately named folder and drag 2.10 into it after it has is included.
Next, I've found it's necessary to adjust the paths for GRASS and SAGA tools under Processing / Options.
Another option, though I haven't tested it myself, might be to install the Boundless version of QGIS. Unlike the KyngChaos version, the Boundless QGIS allows you to drag and drop the QGIS application wherever you'd like. This might be a safer bet, because Boundless is self-contained, in that it is includes with it all the requirements, like GDAL.
Update 1: After additional testing, I've discovered issues with things like running Processing-based scripts. Also, Kyngchaos has recently updated the QGIS packaging for LTR (2.8) and notes the following:
...I also added a note to the first readme about installing multiple versions of QGIS, basically, don't.
Here is the link to the full post.
Update 2: I downloaded Kyngchaos QGIS LTR 2.8 in order to read the full readme. Here's the full explanation as to why multiple versions of QGIS is problematic:
If you rename an installed QGIS before installing a newer major version (i.e., 2.8->2.10), be aware that they use the same preferences and plugins, and there may plugin or preference incompatibilities. Especially with builtin plugins that may store the path to a support executable in the QGIS app package, even if it’s the default and you don’t explicitly set it - you could end up with one QGIS app executing an incompatible plugin program in another QGIS app.
Best practice: don’t.
Update: Boundless desktop versions 1.1 and 1.0 works on the current version of Mac OS.
I don't have an iMac, but according to QGIS, 2.10 doesn't work on Yosemitee, only on Mavericks, Mountain Lion, and Lion.
Download for Mac OS X
Mac Installer Package for both OS X Mavericks (10.9), Mountain Lion (10.8) and Lion (10.7).
This version requires separate installation of dependency framework (GDAL Complete) , also found at the download link below.
I'll just provide a slight alternative to the answer by Tele-Pet. Presently (2017), the easiest option would be to install qgis via homebrew and/or Boundless Desktop (because of the install and uninstall ease). KyngChaos is still good though.
As Tele-Pet mentioned, all QGIS versions will share the same configuration path (~/.qgis2 in linux systems). This can lead to quite a few issues, particularly if we're dealing with different major versions, or you want to have different configurations. Luckily, we can overcome this easily: Instead of launching QGIS from the finder, launch it from the terminal with the '--configpath' variable. This allows you to switch configs. You can run the same QGIS with different configs, or keep separate installs from interfering with each other. In my system, I have an alias in my .zshrc like so:
alias qgisBoundless="/Library/Boundless/Desktop/1.0/bin/qgis --configpath ~/.qgisDB"
Homebrew's QGIS will continue to use the default ~/.qgis config directory. Furthermore, the Boundless QGIS will use different frameworks and even a different python, so you have an extra level of separation (KyngChaos does the same). I could also have added different environmental variables to the alias. That's as much separation as you can have at the moment.
Note that all versions installed will nevertheless share the same qgis preferences files in the Mac's Library. This shouldn't affect much though.