AFAIK RavenDB, which describes itself as a "2nd generation document database", does exactly what you describe. Whenever you run a query that's missing an index, it will automatically create a temporary "dynamic index" to service it. If it finds that this index is used a lot, it will automatically promote it to a permanent index. I haven't tried it yet however so can't comment on how well it works.

But yes, generally speaking, I'm also surprised to see that in 2013 we're creating our indexes manually. While there are of course applications where you really want to ensure that all the right indexes are created ahead of time, for most applications having indexes created automatically based on query patterns would seem like a much better solution.