A lot of people do not want Skyrim to be an MMORPG game, and I am one of those people. However, I think it would be cool to have co-op multiplayer. What I mean is you could invite up to four (or more) friends to play Skyrim with you online. Everything will be the same as in single player, except with more people. I was thinking about it one day while playing Oblivion, and I thought it would be awesome if your friends could join your game and help you through quests, loot stores, search for valuable items, ect. But, the more people you have in your game, the more enemy NPC's there will be in quests, bandit camps, and so on, so that the game doesn't get too easy. The same goes for valuable items, or just items in general. For example, if you are playing with two people, and you both find a really good sword. When you pick it up it will be given to both of you so that it is fair. Or say you and four other people are looting a house. Whatever you steal from the house will also be given to the other player(s), and then they will be able to drop it if they choose. Also, I think regular items should eventually respawn in their original spots (This doesn't mean that it will be taken from your inventory, but simply that another identical item will spawn in its place). For example, you pick up a bottle of wine off of a counter. Another identical bottle will spawn in its place without taking it from your inventory. Well, what do you think? A good idea or a bad one?
P.S.
I saw a thread a while back suggesting matchmaking for the arena. I think that's a pretty good idea! And there should also be a rank system where you can only fight people with the same rank as you so that a brawler isn't going up against a gladiator. And there could also be different types of matches:
1v1
Team 8v8
Players vs. NPCs and so on.
TL;DR:
You have the choice to play co-op with up to four different friends.