I thought of another highly recommendable anime. Although, you're going to have to get the fansubs or the japanese DVD's of it because it was never licensed. It's called Spiral: Bond of Reasoning. It's 26 episodes long. It's a mystery genre for the most part. Every episode or every few, a new puzzle is introduced, which is part of a larger picture.
The main Character is Narumi Ayumu. He has a sidekick named Hiyono, a random girl from his school. She took interest in him at first because she heard him playing the piano and thought it was very beautiful. She becomes very loyal to him throughout the series.
There's not alot of humour in the anime, although there is a small amount. Nothing particularly funny sticks in my memory though. Generally, the anime has a deeply serious mood, reminiscent of Lain.
Oh yes, then there's the all-important content issue. It's quite clean to watch. There were small amounts of violence, ... there might have been guns but I don't remember. I know there was at least a dart gun.
and someone got shot with it. There is some death, and suspenseful situations, so it's not something you'd watch with your kid sister or something. I really don't remember anything particularly objectionable at all about the series though.
I'm afraid to say anything else about this title because it could be quite easily spoiled. Even if I don't spoil the story for you, I could spoil half the enjoyment and rewatchablity of it just by telling you some other very general things about the series as a whole. ^^; so I think I'll wrap up this review here. However, if you've finished the series, I'd love to talk in private with you, as I have a few thoughts about the ending, and the series as a whole, that shouldn't be revealed here. I'd love to hear your comments about it as well.