There are lots of options you have for checking out the Warcraft lore.
As sommerjj says, you have Nobbel87's youtube channel.
You also have the various wiki sites, which host a large collection of information regarding Warcraft. I find the most notable to be the WoWWiki, which has an extensive library of articles surrounding the history, events, and characters of Warcraft.
Blizzard have a section on their website, where they post short stories and comics. This can be considered a valuable resource, given it originates from the official creators.
If you like reading, there is also an extensive series of novels set in the Warcraft universe. The WoWWiki has a good list of them, here. Many concern major events, while others tell unrelated stories that may tie in to the general lore.
Lastly, it may be worth looking up the cinematic trailers surrounding World of Warcraft. While short, they tease various upcoming releases (notably the release of a new expansion, or a new major content patch), and often show off a massive event in a well put together animated short.
You do have the option to play World of Warcraft, of course, which you have already told us you don't particularly want to do. It is worth pointing out that Wrath of the Lich King moved a fair bit away from the stigma of grind and monotony, while Cataclysm brought an entire rewrite of most of the vanilla world, bringing over with it the dynamic changes made from Wrath of the Lich King. If this is still not an option for you, it may be worth looking up the various instances and raids, as these often represented major events during the course of the game.