Here are some patches for Heroes of Might and Magic III that I've stumbled across.
(Download)
This is a fantastic patch that allows you to run Heroes of Might and Magic III at pretty much any resolution that you desire. It even works fine at up to my native 2048x1152 resolution for me.
In the second image, you can see a small map practically being displayed at once at such a high resolution. I personally run the game in 1280x800 so that it doesn’t knock the shit out of my eyesight :)
As you can see from the images below, the game remains at standard Heroes of Might and Magic III size, you just get to see more of it. Excellent!
Update:
Newer versions of the Heroes 3 HD patch now have a built in no-cd feature and fix windowed mode issues with all colour depths.
(Download)
Personally, I like to play Heroes of Might and Magic III in a window without having to change the desktop to 16-bit and avoid the annoying 65536 colours limitation
This handy utility allows you to paly Might and Magic III in a window while also having the desktop remain in 32-bit colour.
Apparently this utility can be used in conjuction with the Heroes 3 HD patch from above, but it only crashed for me. I take it that it's outdated, which is a shame. Larger resolutions in a windowed mode would be great.
Update:
This patch has been pretty well superseded by the Heroes 3 HD patch above which has this feature and much more.
(Download)
In the Wake of Gods is a free unofficial expansion designed to allow the addition of scripts via the Event Related Model (ERM). Some of the enhancements that WoG brings to the table are much needed, basic features missing from the original game-play such as a "purchase all creatures" button, the quick combat option, etc. as well as some medium-level additions such as the Artificer, a new structure for upgrading, combining and changing items, new bonuses for artifacts, skills and so on, while other additions allow some fairly radical game-play changes, such as adding creature stack experience, a third level of upgrade for creatures, etc.
I must admit, the first time I gave this expansion a go, I really didn't get on with it, but I was really looking for a new experience in HoMMIII so I ended up revisiting it. All of the features that WoG brings to the table can be turned off, and you may find yourself adding the features back in once you get used to the changes anyway.
Initially, the "WoG Options" is somewhat overwhelming (Part of what initially put me off), but take the time to give the options a quick read and you'll soon have it all figured out.
Note: The Heroes 3 HD patch above also works with this expansion.