[Itaxpica]

Heroes 3 did have multiplayer via LAN, and IIRC it had online multiplayer as well. It worked pretty well for the time; the fact that the game is turn-based probably helped in that regard.

[kzrdude]

And it has hotseat - players taking turn at one computer, that was the mode me and friends always played.

[gspr]

I think the number one after-school activity for me and my friends was at some point HOMM 3 (and 2).