I'd seen the opening cinematic of the Burning Crusade about 20 or 30 times (including in hilarious Gnome form), but after finally installing and repatching the expansion yesterday, I was pleasantly surprised when Illidan's voice spoke to me from beyond the portal, and the intro movie played out in fullscreen, high-resolution glory. By the time "You are not prepared!" showed up again, I was ready for some Warcraft.
And just in case you want to see it one more time, Drysc offers the following tip on the forums: Whether or not the movie shows up is controlled by a small file in the WTF folder (in your World of Warcraft install) on your computer called config.wtf. Just open that file up in Wordpad (or your text editor of choice. Change the "SET movie" line in there from "0" to "1", save the file, and you're ready to watch it all again whenever you start up the game.
Of course, if you're as cool as me, and you bought the Collector's Edition, you can also find the cinematic (along with lots of extras) on the included DVD-- in fact, it's the first thing you see when you put it in. But it's good to know that if you need to watch the movie in its computery glory, you can.