I just downloaded the client from software update (via @RobertHammen's suggestion),
from the .dist file that is included with that download, it looks like the package won't work on 10.8 or lower....
So it looks like it will probably work on 10.9.x and 10.10.x (haven't tried it yet)
Older systems must be stuck at 3.7.x Client
Hmm, the update is presented to me on a 10.8.5. system and the byte count is identical to those downloaded on 10.9.5 and 10.10.1. I was able to install the .pkg I downloaded on a 10.8.5 system on 10.9.5 and 10.10.1, so it seems to be pretty universal. 10.7.5 and earlier are obviously left in the dust...
How to update
If you purchased Apple Remote Desktop from the Mac App Store, this update appears in the Updates pane of the App Store.
If you installed Apple Remote Desktop from a physical disc, update your Mac to OS X v10.10.2, then check the Updates pane of the App Store window. After updating OS X Yosemite, the Mac App Store allows you to upgrade to newer versions of some Apple apps including Apple Remote Desktop.
After updating, Remote Desktop appears in your list of Mac App Store purchases. You can install it on other computers you own by logging into the Mac App Store using your Apple ID. You no longer need to enter a software serial number to install your copy of Remote Desktop.
OK, I can confirm, if you are running Yosemite 10.10.2:
a) copy your non-App Store Remote Desktop.app into /Applications
b) open the Mac App Store. After a few seconds of chugging, it should show you at least one update
c) it will let you "adopt" the app, and may ask you to sign into the App Store
d) Remote Desktop will now appear in your purchase list
e) you can actually install the latest version onto 10.9.5. The adoption process won't take place on Mavericks, or apparently even Yosemite prior to 10.10.2.
ARD Vn 3.8 is now quotes as Yosemite compliant
We find ARD still to be very useful, and I am glad it's still around.
The functional improvements are important.
However I think the Vn 3.8 makeover looks pretty awful !
I wished they had simply left the menu bar alone..
All the Menu bar coloured icons are now "Black & White Line Art"..
A bit like in Mac OS 6 - ( That's before OS X.. )
They now all look fairly similar, making it easier to accidentally click on the wrong one..
Definitely a backward step as far as User-Interfaces are concerned..
I can work with it if I have to, but I am not liking it.
I much prefer the ARD Vn 3.7 menu bar appearance with it's coloured icons..
So minus two stars.. for the trashy icon downgrade..