When someone asks for the top recommendations on various forums, I always tend to forget one or two that I really like, so now I'm writing them here so that I can go back and edit when I realise I forgot one.

Manga:

1. Nausicaä of the Valley of the Wind

Hayao Miyazaki's masterpiece is a 7-book epic of post-apocalyptic science fantasy world, where a large part of the world is covered by the toxic jungle called the Sea of Decay, and mankind is left fighting for the small inhabitable parts that remain.

2. Yokohama Kaidashi Kikou

This is a sublime manga that moves at a stately pace, focusing on the robot Alpha who runs a café in the nicest possible post-apocalyptic setting you could possibly imagine. A lot of cities are underwater, and life for the remaining people is slow and sedate. Alpha meets people, falls in love, and simply lives in her house and goes on trips on her motorcycle. I recommend trying to find it, because it's one of a kind.

3. Antique Bakery

A pitch-perfect 4-book series about a man who hates sweets and runs a French-style bakery with his colourful staff. By Fumi Yoshinaga, who also wrote the excellent Ooku.

4. Hikaru no Go

This, to me, is the perfect sports manga, which also introduced a great many westerners to the classic Asian boardgame Go (or Paduk or Weiqi). A boy (who's a bit of a brat) gets haunted by the ghost of an ancient Go master, which ultimately puts him on the path to becoming a Go pro and an intense rivalry with the serious Touya Akira. Illustrated by Takeshi Obata of Death Note fame, who really developed a lot over the course of the series.

5. Sweet Blue Flowers / Aoi Hana

Sadly not available in stores in English, this manga follows two girls who go to two adjacent schools, their friends, the annual drama festival, and a whole lot of girls in love. I wholly recommend importing it and finding online translations!

Anime:

1. Revolutionary Girl Utena

One of these days I'm going to write an entire article explaining my love for this series. For this short list, suffice to say that what seems like a simple spin on a classic Prince Charming motif then spins it around a few more rounds and leaves me still thinking about it ten years later. It also made me get a tattoo. Complete with a set of broken, complicated characters and unreliable narrators aplenty. From the director of Mawaru Penguindrum, it also has great visual style and symbolism (just don't watch the movie first).

2. Hikaru no Go

Yes, it's really that good!

3. The Twelve Kingdoms

One of the best fantasy series out there (which reminds me I need to rewatch Scrapped Princess), which is only brought down a bit by the fact that they didn't pull off the middle parts that didn't focus on Yoko as well as they could have. A girl is brought to a strange fantasy world after monsters start fighting on the roof of her high school, and she has to overcome her (serious) self-doubt to prevail.

4. Princess Nine

Okay, so I'm from Sweden, where we have no baseball tradition at all, but dang if this show didn't get me interested in the sport. A girls school starts a baseball team to compete in the boys' tournament, and overcomes both lackluster animation and cheating opponents to make it... well, you'll see how far they go.

As I said, not really a definite list, and I'm pretty sure I forgot plenty of series when writing this list. Like Gunbuster! And maybe X, confusing mess that it is? Maria-sama ga Miteru? Ikki Tousen (just kidding!)? The #1 positions are pretty much set in stone, though.