I've been dealing with an issue for a very long time, I feel like it used to be a problem randomly, but at least for the last few months it's persistent. The Finder no longer lists mounted Disk Images (.dmg files) in the sidebar. Not for DMGs, nor external hard drives / external media.
The volumes are listed in Disk Utility, and I have resorted to using that to gracefully unmount the disk image. When a volume is mounted, it is possible to access it by it's /Volumes/<Volume Name> path.
In this screenshot you see Finder's Sidebar preferences. You can see that I have a DMG for Clementine open, and Disk Utility confirms that. But the volume isn't showing up on the sidebar. You can also see that the Devices list is expanded, listing my built in volume.
I've done some light searching of options to see if it could be controlled by a plist defaults setting, but I haven't found anything yet.
Why aren't mounted volumes showing up on the sidebar? How can I restore them in the list?
This problem began under Mavericks, and has persisted in Yosemite.
Best Answer
Update.
Just realised that it the CDS,DVDS, and iPod option in the Finder side bar prefs control showing of DMGs
You need to check it to get them to show up.
The below may be related to External drives not showing up.
If you drag them of the sidebar they will never show up even when mounted.
To get them back you need to mount them and drag them back on.
This may not be what is going on with your if this is happening to any new items you have never mounted before. But you could try this and see.
Here for illustration a Partition and a DMG being dragged off. (But this has happened to me without me realising or for some unknown reason.)
To get them back I would need to drag them back.
I go to my device window:
And drag them back to the side bar
And now they are back.