Bungie has acknowledged issues that are preventing PlayStation users from logging into Destiny. Issues impacting players' ability to sign in to Destiny were originally only on PS4; however, it appears that the widespread PSN outage is also affecting PS3 users.
We're currently investigating issues preventing PlayStation users from signing into Destiny.
— Bungie Help (@BungieHelp) October 28, 2014
Although the developer didn't blame PSN for the login issues, it's likely that the connection issues plaguing PSN are the root of the problem. Users first begun experiencing problems with PSN earlier this morning following the release of the PS4's latest update (version 2.0, aka Masamune). The addition of Share Play, a new feature added today which allows PlayStation Plus users to stream games and play together, is likely causing a strain on the PSN servers (this is only speculation as Sony hasn't confirmed this to be the cause). As a result, PSN is currently down while Sony investigates the problems.
Potentially adding to the problem is the fact that Bungie pushed live a new update today for Destiny that aimed to create "a more stable experience for all players."
At this point, gaming on PSN is just a giant mess, so everyone just relax a bit. Feel free to vent below because right now there's not much else you can do. On the bright side, when you are able to log back in to Destiny, you'll have an awesome Halloween treat waiting for you.