There are games that you play when you're younger that can have huge impacts on you, that you'll always look back on fondly. I've got a few; Alpha Centurai, C&C Red Alert 2, and more relevantly, Heroes of Might and Magic 4.
Eador: Masters of the Broken Worlds for me has hit on many of the reasons I loved HoMM4, and expanded on them beautifully. I'll start from the top; you are one of the newer demi-gods, and your job is to lead heroes to conquer loose fragments of the world and join them to your own shard. So far so good.
Every fragment that you want to capture involves hours of play, with individual shards giving you random assortments of resources, enemies, and terrain. You have to hire heroes, capture territories with resources, build buildings to give you more magic or troops, hire troops to patrol territories, clear out dungeons in a territory, explore for /more/ dungeons in a territory...yes, small, this game is not.
Some people won't like this game. You can't really pick it up and play for half an hour. This is very definitely an Epic sized game, and personally, it's wonderful.
Combat is done on another hex grid, with all of your party and all of the enemy party lined up on opposite ends of the map. You move, cast spells, fire arrows, the usual deal in a turn based manner, and beware; the AI archers love killing your mages. The heroes you hire will adjust how the battles go; a scout can clear off the enemy mages and ranged units, a warrior is a great front line troop, mages can be skilled in one of several schools of magic (the choosing of which adjusts several other stats) and Leaders serve to make your troops that much stronger.
There are a lot of resources and systems in the game; the mentioned resources, such as Iron and Horses (with plenty of fantasy exotics as well), Happiness, and Karma. The last two aren't terribly well explained, although naturally I was only playing an early release, so I'm sure it will be touched up.
It is possible to speed the game up a bit; you can have the battles auto complete. Of course, you will lose more units this way, and since recruiting away from your home city is a pain, you won't want to much (at least early on). So assuming you're manually controlling battles, there is a staggering amount of time you can sink into this game.
I haven't even mentioned the RPG side; each of your heroes can level individually, and you have to chose where to spend each level out of a pool of 3 randomly chosen skills. Once you hit level 10, you can specialise your Hero into another 4 possible classes; do you want to be better at scouting and sabotage, or have the ability to shoot twice in a turn? Units that you hire can also level, increasing their stats, so that one minotaur you've had for ages is /very/ worth keeping.
I really can't emphasise enough how much depth there is to this game. If you're a fan of the older HoMM series, and thought other hex games like Civ 5 were a little light for your taste, or just not fantasy enough; this is the game you want to look out for.
I feel I should add a footnote for the graphics and audio, since people might be interested; in both cases, I'd rate them as middling. Neither concern me at all though, given the gameplay. The music is certainly pleasant enough and scene-setting, but I think after the 40 hours you will spend /starting/ your first campaign, you'll want to listen to something else for a bit.
Definitely a game to keep your eye on.