Title says it all. Is their any penalty for dying in the original Diablo (monetary, experience or otherwise)?
If I remember correctly, the only penalty was that your items stay in the place where you died.
Comparing to Diablo II if you quit the game and start it again, you body will NOT appear in town.
Found this thread where they discuss the same thing as you asked: http://diablo.incgamers.com/forums/showthread.php?682535-Death-and-Dying
When you die in Diablo 1, you are dead. You have to reload the game from your last save, otherwise you can "start new game" from the character menu with that character, keeping all your stats, but losing your quests, progression, etc.
Playing on multiplayer enables the dungeon shortcuts automatically (crypts, caves, hell) and you can use them at your leisure provided you meet the level requirements. In addition, death in multiplayer results in your items being dropped, which made pking for sport and profit a rather enjoyable activity.