I usually don't like watching anime made from manga, just because a) I like manga art better, b) the voices always startle me because they aren't exactly like the ones in my head, and c) the pacing feels off (it takes about two episodes for one volume, which I can read in half an hour).
I am going to completely eschew plot summary and link you
here instead, as the first five volumes cover the first volume and a half of the manga. Mostly, all you need to know is that Yuuki is our innocent heroine, Zero is the broody grumpy vampire hater, and Kaname is the overly protective vampire who saved kid!Yuuki.
The switches between SD comedy and Gothic vampire crack worked a lot better for me in the anime, largely because in the anime, each mood takes more time, as opposed the manga, which often flip-flops between mood every other page or so. Also, the sound effects help. But mostly! We get many shots of vampires with glowing red eyes!
And! And! People! There is organ music for the big emotional moments, or the little emotional moments, or really, any moment that involves over-the-top Gothic settings! And! The ending song is set to an extremely creepy scene in which Yuuki is a doll dressed in black, Loligoth style, and she cries tears of blood while her stuffed rabbit's eyes glow red! It is AWESOME!
I cannot wait until SPOILER SPOILER SPOILER SPOILER!
Please no spoilers for the manga in comments unless it is under spoiler text.