Death Note in its first episode carries many of the trappings of greatness. From opening theme to ending theme it is packed with mood and philosophical questions, delivered at a decent pace. The storytelling is good, with a lot of scene-setting done tastefully or even sometimes subtly. This may not sound like exuberant praise ("just good?"), but being above mediocre in this department isn't common for anime. The imagery and soundtrack are noticeably good, too, and the premise is interesting: a grim reaper drops a magical notebook; an arrogant try-hard finds it and discovers that he can use it to kill anyone he wants with no apparent consequence. He sets about cleansing the world of criminals, and, after meeting the grim reaper in question, declares that he will become the god of a new era of pleasant humans.
Now, if your stomach turns at the slightest tinge of the supernatural, feel free to check out here, but otherwise, damn! What'll happen to this high school honor student and his plan for global domination? How will his horrible politics shape the world? Given that this is just the first episode, we have to assume he doesn't immediately succeed—what kinds of hurdles await him? Rare is the first episode that leaves me wanting more!
Recommend: Yes.
Rewatch Disclaimer: I watched all of Death Note back when it aired a dozen years back, and it has some good stuff. But its treatment of female characters is ... lacking, shall we say, and also it devolves into tedium and shark-jumping about two thirds of the way in.