It's working for me now. Had couple of app updates pending. Completed them.
Went to settings/application manager/all/video player/clear data.
Restarted. Works great now.
Same issue with my Sprint S4 too.
Same with all streaming videos, not just Youtube.
Still have my unlimited plan, so it is ok for the time being.
Looks like Verizon S4 guys reported it too..