While I wouldn't call all of my suggestions smart or "Deep", they're different and intelligent enough to stand above all of the Shounen/fan-service shows out there;
Durarara!!: Set in the mid 2000s, this is the story about the Ikebukuro district in Tokyo and the people and groups of people in it. There's not one specific main character in the story, but every character has his or her spotlight and their own back-story that reveals more about the world and the plot.
Now and Then, Here and There: Young boy sees young girl. Young boy climbs to the top of a smoke stack to talk to young girl. Young boy and young girl then get attacked and pulled away into an alternate dimension where the young boy is forced to join the child army of the most powerful and insane dictator that dimension has ever known. It also might be important to add that this anime takes the premise entirely serious and there is absolutely no comedy whatsoever. It's glorious, it's horrifying, and it's absolutely brilliant. Also, the American dub is pretty good too.
Serial Experiments Lain: Alright, this may be the "Are you being pretentious?" pick of the bunch. The story begins with a girl (called Lain) who starts to get mysterious emails from a dead classmate...and that's all I can tell you about the story without getting into spoilers and interpretations. This is by far the most bizarre and weird anime I've ever seen, but that's what makes it so appealing. If you're into extremely outlandish anime, this may be the perfect show for you.
Digimon Tamers: Alright, this is almost entirely put in her because of nostalgia, but the show does have some very good things about it. I can't quite tell what those things are, but the show is genuinely good. However, you may want to watch the first two seasons of Digimon (respectively Digimon Adventure and Digimon Adventure 02[footnote]You may just want to look up character bios and plot summaries for this season since it's complete rubbish and not worth your time.[/footnote]) to understand how the Digimon stories have worked before it and there are a few jokes and tid-bits in Tamers for the fans that did watch the shows. Also, you should know the difference between a digimon tamer and a digi-destined; digi-destined are chosen individuals who are called upon to battle a threat to the digital world while digimon tamers are just individuals who happen to have a digivice and a digimon. Also, if you haven't realized this by now, I am a complete Digimon fanboy.
