In between the weather knocking out my power here in Milwaukee, WI, I managed to sit in the dungeon queues long enough to discover that ... they're broken! Thanks to Lord Ahune, instance servers are overall stressed beyond capacity despite Blizzard's constant upgrades over the years.
It looks like overall it is due to the influx of everyone running the Fire Festival encounter, plus arenas, and normal dungeons.
Our Realm Technicians are looking into it and making what adjustments they can to improve connectivity and performance. If more information becomes available we'll be certain to pass it along.
We have no ETA on when the situation will be resolved, but the most recent post in the above-linked thread was a mere 5 minutes ago
as of this writing, so it continues to be an ongoing issue.