I love the cinematic art look of early '00s supernatural/sci-fi anime series like Blood - not that DoD is really in the same class (Blood's Viet Nam-inspired visuals were truly stunning), and DoD's establishing shots and cool, fast steadicam-type dashes down corridors contrast in a kicky way with the utter unreality of anime-world tropes. Also, as an earlier reviewer says, the universe has a fun, Beetlejuice-type of "omg, even AFTER we're dead?!?" comic universe, which for me works as further compensation for the sketchy plot. The Japanese voice actors are typically good, too... and who doesn't love shinigami?? Between this, Death Note, and Bleach, I've gotta say that the versatility and power of your average shinigami make Western zombies and vampires seem sadly limited and low-rent.
So, if you appreciate not-scary supernatural stuff on occasion, can dig yaoi-lite, and love impossibly pretty anime people (the leads' violet and green eyes are insane), this is great low-stakes fun. Having seen relatively little anime aside from super mainstream shows, I do know that DoD is not a Stellar Work of Genius, but sometimes it's nice to just sit back and know that the characters are always going to be Fine at the end.
