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#11
I bought Heroes III Complete from GoG.com as well and have been playing it (with limited success) on Windows 7 Home Premium x64. I have set all the .exe files in the game's directory to "Run as Administrator" and Compatibility with WinXP SP2. I can usually get anywhere from two to four hours of gameplay in before it crashes and I have to reload from the autosave.
After emailing GoG.com's support team, they replied that they don't support Windows 7 yet. So warning to anyone buying from GoG.com, your games might not work on Windows 7. So far I'm 1 for 2.