UPDATED: This issue has now been resolved, and you shouldn't have any problem accessing the PlayStation Network.
Original Story follows...
If you've just switched your PlayStation on, and realized you can't play certain games, it is because PlayStation Network (PSN) is currently experiencing problems.
PSN Is Currently Down
According to the PlayStation Network Service Status page, certain parts of the PlayStation Network are currently unavailable to users and have been for several hours.
According to the Gaming and social section of the service status page, "you might have difficulty launching games, apps or network features." What exactly these difficulties are we don't know, games could actually launch slowly, for example, or not launch at all.
It also isn't clear whether the outage affects everyone. This writer has launched and played Call of Duty Black Ops: Cold War multiplayer successfully this morning, so presumably it is only certain members of the PlayStation community who the outage is affecting.
According to the status, affected platforms are PS Vita, PS3, PS4, and PS5.
Are Other PlayStation Network Services Affected?
Looking at the service status page, no; the outage has impacted only gaming and social. So account management, PlayStation Now, PlayStation Video, PlayStation Music, and the Store all remain in peak health... up to now.
Sony is currently working on resolving the problem with the gaming and social elements of PSN. You'll just have to try to remain patient for now while Sony sorts it. You don't actually need to do anything other than sit tight.
Hopefully PSN Will Resume Full Service Soon
Anyone who remembers the month-long major PSN hack outage of 2011 will probably shift nervously in their seats at this news. However, given that most of PSN is up and running, we can't see this being as much of a disaster as the down-time a decade ago.
Why not use the time to optimize some settings on your PS5, if you have one, or sort through your PS3 or PS4's hard drive and have a clear out? It pays to keep your console free of clutter.