There have been a couple of posts about various issues in high resolutions particularly with windows 7 and 8 so here is what I have learned from this forum and external boards that worked for me.

Flickering
If you set the game to its highest native resolution or use a custom high resolution the game will flicker, there are two solutions here, if you exit the game and restart it will work fine or you can alt-tab or windows key to desktop and then click the game icon in the task bar and the flickering will stop.

Custom resolutions
For custom resolutions change the target in your shortcut, the original gog target looks something like this....

"D:\GOG Games\SimCity 4 Deluxe Edition\Apps\SimCity 4.exe" -CPUCount:1 -f

My working custom resolution looks like this...

"D:\GOG Games\SimCity 4 Deluxe Edition\Apps\SimCity 4.exe" -CPUCount:1 -f -CustomResolution:enabled -r1920x1200x32

Window mode
If you want to run in a window you can use the windowed mode shortcut for the game that can be found in the gog folder in the start menu or change your target to look like this...

"D:\GOG Games\SimCity 4 Deluxe Edition\Apps\SimCity 4.exe" -CPUCount:1 -w

Or for a custom window

"D:\GOG Games\SimCity 4 Deluxe Edition\Apps\SimCity 4.exe" -CPUCount:1 -w -CustomResolution:enabled -r1024x768x32

Game performance
Some people are reporting the game may work better in a window if you have a lower end machine and your city gets very big, it has also been reported that higher end machine are slowing also in some cases so swapping to window mode may be a solution if this happens to you.

Supported Resolutions

1280 x 800 (16:10)
1440 x 900 (16:10)
1680 x 1050 (16:10)
1920 x 1200 (16:10)
1024 x 576 (16:9)
1360 x 768 (16:9)
1024 x 600 (16:9)
1600 x 900 (16:9)
1920 x 1080 (16:9)
1920 x 1200 (16:9)
2048 x 1152 (16:9)
1366 x 768 (16:9)

While some resolutions are supported, some clipping of the interface may occur making it impossible to control certain functions, such as "raise mountains" in 1024x600 for example.

I hope this info is useful, if I find out anything more I will add to the post.

I might be wrong here, but I think the game only "supports" the resolutions that one's adapter and monitor support, even in a window. For example, I don't think I was able to run it in 1280x800 or 1440x900.

I've not tested the resolution my self and I would agree they have to be supported by your hardware although I'm not sure about window mode as with some games I have managed to run in some odd resolutions in the past. All I can tell you is that these have been tested at widescreengaming.net and shown to work, I tend to stick to more standard resolutions my self.