Over the last twelve hours or so, people trying to play Destiny 1 and Destiny 2 have had trouble connecting to the game, but at last Bungie support says it has found a resolution. However, fixing the issue in Destiny's "core services" required restarting the servers and kicking everyone out again. So if you'd finally managed to log in and are now looking at a loading screen again, just give it a minute and keep an eye on the Bungie Help Twitter account for updates -- you'll get to those daily bounties soon.
Update: In a subsequent tweet, Bungie said the downtime is expected to last until about 7 PM PT / 10 PM ET.
Update 2: Now the repair period has been extended through 11 PM ET, we'll see how much longer it takes.
Update 3: It took past midnight, but both Destiny and Destiny 2 services are restored.