Wurm Online & Wurm Unlimited
Wurm Online is probably the only real sandbox survival game that still exists. You can build what you want, where
you want and you can even dig up the dirt and shape the land as you like. The graphics are a bit old but Wurm is constantly
being upgraded nearly every week. If you like to have your freedom building things you might want to try this game.
While there are several official online servers, the developers have now made Wurm Unlimited, which contains about 95% of all the online features, 5% NPC's the player can interact with (you can even chat with them, although most of what they say is pretty weird) and it is a singleplayer or can be played with friends on dedicated servers.
At the moment I only have a short story from one of the so called Impalongs which are held on the official servers in Wurm Online during special seasons (like christmas). Those Impalongs are events/festivals made by players for the players, often with support of one or more gamemasters who summon monsters for the party.
The story is linked in the side navigation.
Lord of the Rings Online
Lord of the Rings Online is a MMORPG, but even
if you want to play alone you are able to do so. After several updates at least the epic story is turning into a singleplayer
RPG, you are not forced to play in groups, even if the most instances aside from
the main story are group content.
You can play this game from character level 1 to 75 (June 2012), once you've reached a character level of 20 the first group instances become available. With your character advancing through the story and game, more instances will fill this list.
There is also a skirmish option where you can play several areas in skirmish mode, alone or with a group. Within those skirmishes you can summon a special soldier that will help you during the fights. With the last update of the game you are now able to summon this soldier also in the normal landscapes (it costs Turbine Points then).
All in all the Lord of the Rings Online is a pretty good game, the designers made a very good job, landscapes, cities, every detail is a beautiful piece of art somehow. If you are Tolkien fan you will be happy to see Tom Bombadil or even Aragorn who sometimes needs your help while the fellowship is on it's journey towards Mordor.