Strongly recommended

1. Heroes33.exe -- Removes the differences between versions of the game (between 3.2 and smaller, You don't need it for 4.0 and 3.2). It allows you to start the game without the CD. Put in main Heroes III directory. To play on gameranger you need to change name to heroes3.exe.
2. CrAnim -- Speeds up the movement of units in battle. Put in Heroes IIIData directory.
3. HoMM3 Lighter 1.5 -- File enables to transfer by one click all army (f10) or artifacts (f11) between heroes.
4. CrBanks -- contains all informations about banks (location where you get reward for fighting in it). Changed: reward from naga bank is in gems instead of sulfur, because this was mistake of creators. Put in Heroes IIIData directory.
5. Objects -- contains all objects in HoMM3. This one is without obelisks, cartographer, hill fort (thanks to that, regulations are shortened), keysmaster's tents and border guards; adds crypts on lava, wastelands and undergrounds. Put in Heroes IIIData directory.

Other recommended

1. Files World of Heroes -- default files for friendly polish WoH league since 4th season (2011 year). Put all in Data directory.
   

   Deteailed description

   CrAnim, CrBanks, Objects - same as above.
   CrTraits - reduces phoenixes and firebirds growth to 1 with fort.
   ArTraits - all about artifacts. Changes: on map there is no artifacts with necromancy, diplomacy, navigation, eagle eye, also no angel wings and boots of levitation. Price of this artifacts is halfed. +5% and +10% resistance artifacts major(3lv)->minor(2lv), endless sack of gold relic->major, boots of speed minor->major.
   SpTraits - includes all informations about spells. Changes: in town guild there is no waterwalk, scuttle and summon boat; magic mirror is now 3lv spell.
   HcTraits - file includes heroes' informations. This changes that while level up, necromancy, dyplomacy, navigation and eagle eye chances to gain are 0%.
2. Heroes 3 HD -- HoMM3 High Resolution Project. Mod that has option to choose resolution even 1440x900, and amazing changes like transfer all units or artifacts with one click, fast army split by ctrl+left click, shift+click, and fast gathering units of one kind together by alt+click. Unfornately it has many bugs, sometimes destructive for gameplay, so we wait for more and more perfect versions.
3. Heroes 3 World Tournament -- list of changes -- especially look at simultaneous turnes option and permanent autocombat that you can play at your own if unit's loses are too bad for you (even half of the game time less together!). There are many controversial things too, like stronger unit's specialists, slow 2lv guild and scrolls->gold piles.