Higurashi no Naku Koro Ni - its plot is so sophisticated, one has to actually rely on info from the game on which the anime is based to make full sense of it. This is also a drawback, of course, but thanks to some dedicated posters, the AS Higurashi forum has the info that I anm referring to. So if you liked the mystery aspect of
Monster, this can be a great choice.
Death Note - personally I think this series is vastly overrated but it can be addicting indeed, especially if one is not as cynical as me and is not purposefully looking for plotholes all the time.