Chicago does it one way and AP does it the other.

I definitely prefer it un-spaced, though, personally.

MLA and APA as well as Chicago.

I think this is a localisation issue; in the UK, it's much more common to see space-surrounded em dashes.

As far as I know, the UK styles that recommend spaced dashes are using en dashes where US English would use em dashes, and the ones that actually use em dashes, like Cambridge or Oxford, are unspaced.