Blizzard has posted Chapter 2 of their little "Rise of the Lich King" series on the official Wrath of the Lich King website. It's called "The Claiming of Frostmourne," and it covers Arthas' descent into corruption, the razing of Stratholme (remember that place?), and the finding of the sword Frostmourne in Northrend.
If you've played Warcraft III, of course, this is all old news, as all these events are actually shown in that game. But if you haven't played Warcraft III (and its expansion, the Frozen Throne), now might be a good time to do so. While the Burning Crusade reflected more old school lore, including the creation of the Orcs and the opening of the Dark Portal, Wrath of the Lich King's history is pretty recent. Yes, Illidan appeared in the expansion, and others in Outland did as well. But since the beginning of Warcraft III, the story has been all about Arthas, and how bad things are done in the name of believed-to-be-good intentions.
With the next expansion, it'll be great to finally return to that story. Of course, my favorite part of Arthas' story is actually the scene that comes after "The Claiming of Frostmourne"-- what Arthas does after he obtains Frostmourne and is corrupted by the Lich King. Echoes of that are still heard (literally) in the world of Azeroth today.