Mistborn, along with Elantris and Warbreaker (and the upcoming Stormlight Archive series), is set in Brandon's fictional universe that he calls the Cosmere. The major common element to these books is the Shards of Adonalsium. The evidence so far seems to indicate that Adonalsium was roughly equivalent to God, though whether he actually created the universe is unknown. Adonalsium is now broken into a bunch of Shards, which are scattered over various planets. Ruin is one Shard, Preservation is another. There is at least one Shard in the world of Elantris, and it is responsible for the Dor's power. There is a Shard called Endowment (Brandon revealed this name in a Q&A) on the Warbreaker world that is responsible for the Returned and probably the whole Awakening magic system.
There are some common characteristics of the Shards that a smart and attentive reader might notice. There is also one character, who has so far always been minor and has not had any point of view scenes, who is able to travel between the various worlds that have Shards and has appeared in all three of Elantris, Warbreaker, and the Mistborn trilogy. Brandon has confirmed that this is actually the same person, not just reusing the name.
Brandon has stated that he has plans for potentially two trilogies of new Mistborn books, but it will be quite a while before he gets to them. The first would be several centuries after Hero of Ages and would feature an industrialized somewhat modern world - with Allomancy and Feruchemy. The genetic heritage of Allomancy would be extremely widespread but diluted, resulting in Mistings being very common but weak and full Mistborn almost entirely relegated to historical legend. Feruchemy would be similarly diluted due to the efforts of The Lord Ruler and Ruin before and during the current trilogy, with the result of Feruchemical "Mistings" appearing (people with just one Feruchemical power) and full Feruchemists with all 16 powers being about as rare as Mistborn. The other trilogy would be set after an additional time gap, going into a more futuristic spacefaring society.