Been a while since I sat down to watch Angel Beat. That anime was good. The first half of Death Note is very good, but it second half is very much a mixed bag of extremely good idea and meh ideas, just trust me when you get to the second and you will know it's the second half keep watching even through the slower episodes because some of it's best episodes are hidden among the second half's mess.
Blue Exorcist is really good too. I could easily put it alongside the others on my previous list. However, there wouldn't be an easy way to describe it in just two words. I will warn you there is a "Sequel" to it that feels very odd in it's starts since it relies so heavily on the manga. Basically the first series ends on an anime-only ending, but that not bad at all. It's ending is by far one of the best anime ending out there, so much so that it actually inspired the writer to make the ending of the manga extremely similar to the original anime ending. This, unfortunately, leave the "Sequel series in a bit of a strange spot on whether it should be watched because it only covered a single arc and just stops. Simply put, watching Blue Exorcist first series and enjoy the goodness of it, but only watch its sequel if you feel you need more, yes it creates plot holes for itself by existing, but it's still more of the anime.