Make sure you are not blocking content.

Start Firefox in Safe Mode {web link} by holding down the <Shift> (Mac=Options) key, and then starting Firefox.

A small dialog should appear. Click Start In Safe Mode (not Refresh). Is the problem still there?

Yes, the problem is still there. I also cleared my cookies and cache a few minutes ago. Still won't play videos.

Type about:addons<enter> in the address bar to open the Add-ons Manager. Hot key; <Control> (Mac=<Command>) <Shift> A)

On the left side of the page, select Plugins. Make sure the ones you want to use are set to Ask or Allow. ++++++++++++++++++++++++++++++++++++++++ Go to the web page. Once the page is loading, mouse to the address bar and Left-click the icon. Select Permissions. In the menu, Make sure the ones you want to use are set to Ask or Allow.

First off, how do I know which plugins I want to allow? I changed the ones that mentioned Adobe and Shockwave to "always allow" but I don't know if any others are related to my problem. Second, when you say "go to the web page" which web page do you mean? Facebook, the one I'm having trouble with? Or some other web page?

TerryRA said

when you say "go to the web page" which web page do you mean?

Any website you are having trouble with.

Ok, I tried that on a couple of videos. It says (Facebook) "You have not granted this site any special permissions." But on the Add-ons Manager menu, there is no Facebook listed. The reason I am really confused is because I used to have no problem. Then about a year or so ago, I sometimes had a problem playing videos that some friends would post from their own phones (homemade). Then, no videos would play for a time, then they'd play again. I did nothing to the inner workings of my computer to change anything, so I imagine it was some type of automatic update or something that did it. But now it's been like this for a couple of months, and it's really irritating never knowing what people are talking about in the videos, and not being able to see recipe or other instructional videos. But Youtube videos play just fine.

TerryRA said

Ok, I tried that on a couple of videos. It says (Facebook) "You have not granted this site any special permissions." But on the Add-ons Manager menu, there is no Facebook listed.

In this case, not the Add-ons Manager, but the webpage. It's possible you need to go to a Facebook page to set this.