I was really looking forward to seeing what Bioware would come up with for April Fools' Day this year - but so far nothing has gone up on the site. Even considering the time zone differences, I would have expected something to have shown up by now. I'd be a little disappointed if they decided not to bother this year. While not really important, April Fools' jokes seem to have become a tradition among MMO developers, not to mention that they present a nice opportunity to remind both players and devs not to take everything about their game too seriously all the time.
2012's Ship Droid Experience is still a classic, and when I went back to re-watch the little videos they released for it, they made me chuckle even now.
Last year's Dance of the Hutts was a bit more subdued, offering no promotional videos or anything, but just seeing those screenshots of characters on their Hutt mounts again still made me smile.
A Google search for "swtor april fools" even brings up results from 2011, before the game was even released - and while I'm not sure whether this actually came from official channels at the time or was just a fan-made thing, seeing random characters converse in the Wookiee language is certainly humorous.
We'll see whether they'll still come up with anything for 2014...
EDIT: They did add something after all, yippee! "Become part of the battlefield with the newest Ship Role: The Asteroid"