I'm not sure, but you'll most likely get more responses if you post in the correct subforum, the
Ailesberry Farm, where there are tons of information on the greatest anime series.
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Here's my take:
I honestly think that it depends on what the person likes. Not only that, but they must be able to relate to the storyline or the characters well in order to enjoy the series. Here's a few recommendations that I can think of.
For the person that likes romance shows, I would check out
His and Her Circumstances and
The World of Narue. Both shows have characters that I can relate to, and also makes a great romance story.
For the person that likes giant robots,
The Big O, the
Gundam series (any one will do), and
Neon Genesis Evangelion are ones to consider. They have a great story along with interesting characters. However,
Neon Genesis Evangelion requires you to have an open mind, so be aware of that when watching that series. If you enjoyed that series, I would also check out
The End of Evangelion, a rather disturbing conclusion to the series.
For the person that enjoys seeing a bunch of girls with one guy, check out
Tenchi Muyo! and
Sister Princess. I've enjoyed these harem series because of how the different characters are all able to love one person. Sadly, this doesn't happen in real life, but it's nice to dream, right?
For the person that enjoys thinking beyond the box,
Serial Experiments Lain is an excellent series to watch. It is a bit techincal in some moments, but you'll still be able to wonder about a lot of things, even after watching it a number of times.
For the person that enjoys sad stories, I can't think of another series other than
AIR. It's quite an excellent series that has great characters, and a great story. It's only available in fansub format right now, so you can see it right away.
For the person that enjoys school life,
Azumanga Daioh,
Super GALS!, and
Cromartie High School are great to watch. Not only do they relate to school life, but also manages to have great comedy at the same time.