Today I got RoA 3 and wanted to play it at once, but alas everytime, when I leave the temple the game starts in, it loads and loads and loads and loads... forever. Has anyone any idea, how this could be solved?
I am using Win 7 Pro 64-bit and usually all games run fine under Dosbox.

To help you, I just installed and started RoA3;
What happens right when you select Leave temple is a voiced cutscene with the priestess. Based on your post, I am guessing that your game is having issues with this particular cutscene.
You get exactly the same cutscene when you attempt to talk to the girl.
Try booting up your game and selecting the Hi button to talk to her and see if you get the same endless load problem.
Also, right when the game starts ( after the intro ), do you see the spinning CD with a goblin running along it for a second ?
Originally I was going to suggest moving the game to a different location on your HD. In particular, try something such as C:\RoA3\ or smiliar.
The reason I was gonna suggest that is because windows has known to deny write access to some applications within the programs - file folder.
But it seems to be more of a problem of reading or sound output rather than writing.
There are 2 dosbox debug files in the RoA3 folder, stderr.txt and stdout.txt , check both of them and look for relevant things.
I would suggest to run some debugging:
Try disabling sound emulation in the dosbox config file;
Try to change the dosbox config file to launch the sound selector , you can do this by exchanging RIVA with "sound". Run the shortcut, test the sound output and for debug purposes disable sound. Then put RIVA again and try again.
There also is a R_PATCH file in the RoA3 folder. I do not know what it does but it might be relevant.
Good luck. Also, the detail view size of my realms3.gog file is 602.366.016 bytes. You might wanna verify that yours is the same size.
Again, good luck!

Thanks, but the cutscene is not the problem. I click the leave button once and I get the cutscene, talk to the priestress and then press leave again. Then the loading screen appears and I see an orc jumping over a sheep over and over again.
But I'll try to reinstall and check the error logs.
Hmm, I uninstalled and reinstalled the game and I noticed something I missed last time. There's an error message showing in a very dark grey showing on the loading screen:
"Assertion failed, Handle file ..\source\realdisk.cpp, Line 262. Press ESC to continue."
And my realms3.gog file is way smaller. I will redownload and install again, I think.

The orc jumping over the sheep means its trying to read from the CD which is appearently failing.
Try making a copy of realms3.iso , mounting that with daemontools light ( if you happen to have that installed , alcohol 120% should work too ), and then installing the game from the mounted image using dosbox.
This will require a tad more dosbox-wizardry, if you need help with it let me know.

Hmm, I might have to try that then. It's something I tried to avoid, but it obviously can't be helped. :P
I'll let you knwo when I got it working.
UPDATE: Installing the whole game into another system helped. Windows obviously prevents the game from running, when it's in the "c:\programme (x86)\" folder.

I just got the game today and the same exact thing happened to me. I changed the Graphic mode in the GOG start menu from "Overlay" to "Direct3D" and it seams to work fine now.

I am not sure if the other suggestions on this thread have solved your problem...
..but I believe I remember having this problem on my first install. My memory is a little rusty (shouldn't be - I bought it only a few months ago...) but I recall that I solved it by setting all .exe files (actually, I note that I have only applied this to the 'dosbox.exe' and the 'graphic mode setup.exe' file in the install directory, but it wouldn't hurt to do it for all, including the install file prior to installing/running everything - just to be sure) to 'run as administrator' and compatability: XP SP3.
Sorry in advance if that isn't the solution, but I did get the same problem you describe, and I am certain there was a reasonably simple solution.

The answer to this is pretty simple. Just right click on the exe file or shortcut for the game application file. Then click on properties and on compatibility. Set the mode to Windows XP, hit apply and ok. Then start the game:voila, you get out of the temple and you're on your way.

Thanks, guys. But when you check my last post, you will realize that I already solved the problem myself. :)
By the way, not using the c:\program files (x86)" folder seems generally to be a good idea.