I changed the display size to 1600x1000, but on every login it changes back to the maximum setting of 1920x1440, so I have to change it back again. I normally only need to do that once or twice per day, but it's becoming a bit of a nuisance. Any solutions?

Now it's much worse. The monitor settings changed to 800x600, and the only other options are even smaller sizes. This happened before and after a few reboots it solved itself - at least, I can't think of anything I did that solved it. All I did was try several desktop environments, so I tried that too this time, but to no avail. Since it's the same in all de's, I suppose it's Ubuntu that causes the problem. Which leaves me barking up the wrong tree here. I'll try another one.

Please remove ~/.kde4/share/config/krandrrc

Also, to ensure monitor settings are applied on login, ensure that "krandrtray" autostarts.

New day, new screen size. When I restarted this morning, it was back to 1920x1440, which I again set to 1600x1000.
I have ~/.kde, not ~/.kde4. I renamed ~/.kde/share/config/krandrrc and logout out and in again. Back to 1920x1440. So I did a complete reboot. Again 1920x1440.
When I look in the processes in the System Monitor, there is no krandtray (or krand-anything).
Note that I don't have /etc/X11/xorg.conf, something that came up at an Ubuntu forum where I also asked this question. However, I do have one from an old Linux-installation. (Not sure if that is Suse or Ubuntu, though.) Might it be an idea to copy that to my present installation?

Copying Xorg.conf is not a good idea.

In your case, simply ensure that "krandrtray" is automatically started, and the monitor settings you make in System Settings will be applied on login.

To make krandrtray autostart, use the Autostart control module in System Settings > Advanced.

I'm running sidux 2010 so don't know if this will work for you . . .

I recently had major problems getting a new Samsung 24" monitor working. It kept defaulting to 2048x2048.

I ended up entering the horizontal and vertical sync rates in my xorg.conf and it's been happy sailing ever since. I do not have any entries for screen display sizes.

Here's my Monitor section from xorg. I'm using an nvidia graphics card:

Section "Monitor"
Identifier "Monitor0"
VendorName "Samsung"
ModelName "SyncMaster P2570"
HorizSync 30.0 - 81.0
VertRefresh 56.0 - 60.0
Option "DPMS"
EndSection

Both VendorName and Model were listed as Unknown. Worked fine that way. I manually changed those.

Those Horz Vert numbers are for my 1920x1080 display. Yours will differ.

Edit: I'm assuming your monitor's native resolution is 1600x1000?