I am looking for suggestions on how the passage of time could be handled in a multiplayer RPG, particularly the ways a players could alter it.

Most single player games allow the player to wait, sleep and/or fast travel, which causes their character to jump forward in time by a set amount to skip the boring parts. If this was allowed in a multiplayer game, players could become out of sync with each other.

Does anyone have any suggestions on how this could be handled (other than not allowing those actions) in a game with 1 to 8 players?

One option is that all players agree to speed up time somehow. This can work if the number of players is not too large. For example, Minecraft allows players to skip the night if all players are laying in beds at the same time.

You could make time travel a part of the game rules, like in http://www.achrongame.com/site/  

I had considered asking the other players if it was okay for one of them to initiate a time skip action for them all, but couldn't think of a way to please everyone if someone refused. This would be even more difficult if the players were split into separate teams doing different tasks.

Achron looks interesting, but it would likely be a nightmare to create an RPG version with any depth. I've added it to my Steam wishlist though, as I do play strategy games from time to time, so thanks for that.

Time can be broken up into segments, like Avalon Hill's phased turns which allowed for "simultaneous time" for both players.  "Artificial time" is the basis of all game and simulation design even if it is as abstract as the "I go then you go" turns that most people seem to think is how all table top games worked.  I have an even more sophisticated way of doing this, but the original basic Avalon Hill concept would work for you.

Each player could have a block of time to use.  This might be a sophisticated phased turn system with a sequence of play, or as simple as having for example 60 "time points" to spend each "turn" taking actions.  In this example a "turn" would obviously be 1 minute.  In an RPG you might say a turn is one week, and each player gets 7 actions per turn.  Players have to wait for all actions to be completed for all players before the next "turn" (ie set of actions) begins.  This can be done in real time, in fact sophisticated enough "turns" are real-time running in slow motion.

There are as many ways as using this concept as you are able too imagine, there is no one way of "doing it right", but a real-time version of Avalon Hill's simultaneous action phased turns would allow you to do what you are wanting to do in a good way.  It can be as simple or sophisticated as you want it too be.

I'm not familiar with Avalon Hill, but I'm not sure that breaking time into segments would help.

I tend to avoid turn-based RPGs as they seem to emphasise the game part much more than the role-playing. For me, it is harder to immerse myself in the world or my character if everything pauses between commands.

The key to doing what you seem to want to be doing is that the players need to keep re-syncing with each other if they are going to need to be in the same place at the same time.  If the players are never on the same screen at the same time in real time then what you want to do is easy, if the players are ever on the same screen at the same time in real time then what you are wanting to do is a lot harder.  So would players be playing independently, or would they be on the same screen at the same time?

Yes, all or some of the player characters could be in the same place at the same time, as playing co-operatively would be an (encouraged) option. Time would only become an issue if individuals decided to do things that take a different amount of time, like sleeping or travelling, and put themselves out of sync with the others.

I would rather not go the usual MMORPG route by removing sleep options, having every shop open 24/7 and allowing players to teleport long distances.

Perhaps it really isn't an issue. I say drop a visual special effect on players that are manipulating time in some fashion. Considering multiplayer, position and orientaion also seems a non issue. Good on you if you're a blur streaking across the screen with that particle emitter working overtime goodness. As long as we're following the game rules, 

Edit: whoops, we're in 'game design and theroy' so apologies if I'm off topic. Another way to express the idea would be super speed (i.e. DC Comics The Flash) to simulate altered time.

I'm not asking about just a few seconds. If one character rests for 8 hours and another doesn't, you can't expect the first player to just sit and wait for the other to do something to make up the time difference.

If you allowed characters to continue playing out of sync you could end up with any number of paradoxes.