As
SMD mentioned, the closure of the Rivers of America (Tom Sawyers Island, Mark Twain, Columbia, and Canoes), Fantasmic!, and the Train have already been announced (see this
Parks Blog post). The Aladdin musical at the Hyperion (DCA) and the Big Thunder Ranch (Jamboree area, petting zoo, and BBQ restaurant) are closing permanently on Jan 10 (last day). The Aladdin show will be replaced by a Frozen musical in the summer (so the theater will be dark while you are there in April).
Those are the closures that have been official announced by Disney, but there are other closures that are listed on operating calendar at this point (but no official end dates have been announced). Jungle Cruise and Autopia are both going down for an extended refurbishment starting on Jan 11, but no official re-opening date has been announced (sometime in April is the most common end date I've seen, but DLR has not official said anything). Splash Mtn is slated to begin a closure on Feb 8, but no re-opening date has been announced. Likewise, Soarin' will be closed on weekdays (but open on Fri-Sun) for an unknown number of weeks (started on Jan 4).
You can look at the
Disneyland.com operating calendar to track "official" information and then sources like
MousePlanet,
wdwinfo, etc. for the latest rumors and best guesses.