Paul and I just finished watching "Noein: To Your Other Self" (2005), and we really really loved it. It's a 24 episode anime series about time travel, quantum physics, and all sorts of amazing cool stuff. It's the first show I've seen that really gave me that feeling I'd get when I watched "Lost", in the best way possible.
It centers around a young girl named Haruka and the sudden discovery of an inter-dimensional traveler in her sleepy hometown. The story only gets stranger when she discovers the traveler is her good friend Yuu, from 15 years in the future.
It's a show that has just the right mix of emotional plot, action, science fiction, real science, and a sprinkling of comedy.
I would say it's a truly amazing piece of animated storytelling. It's streaming on Netflix and I recommend it to all!