Shigofumi

The relationship and personalities (and choice of weapon) of Kino/Hermes and Fumika/Kanaka are very similar. Also the main character will spend time philosophizing about the situations they encounter.

The personalities of the two main character for each series is strikingly similar: the quiet, unmoving female heroine, and her talkative inanimate object of a partner. Kino's story is an episodic exploration of existentialism, so the story goes a little bit slower than Shigofumi, but if you are patient you may like it quite a lot.

Both of these anime revolve around competent, gun wielding women who act a bit like guys. They have an episodic feel to them, although Shigofumi is less so. Also, neither of the main characters judge what they witness, they simply observe. Overall they both have a similar feel and if you liked one you should like the other.

Both Shigofumi and Kino no Tabi have a similar main character. Fumika and Kino are both silent girls with somewhat similar attitude towards world and the philosophy of not getting involved in events surrounding them. Both are accompanied in they journeys\\\\work by a talking item (Kino's motor an Fumika's staff). Although Shigofumi takes place in modern japan and Kino no Tabi takes place in a fantasy world, they both contain interesting (but different) drama. If you liked one, you should check the other one as well.

P.S. Did I mentioned that both are quite grim?

Undoubtedly, those who loved Shigofumi will love Kino's Journey as well, and vice versa. First released as light novels of the same names, both Shigofumi and Kino's Journey feature rather similar main characters -- Fumika and Kanaka, Kino and Hermes. The two girls and the two others are each in a relationship of a wanderer and a guide; the girls roam about, from people to people, from place to place, with their purposes. They have their personal history revealed along the way, but for most of the story, they live the life of wise observers:  indifferent but thoughtful ones who can reflect upon the very question of human nature.

If there is any "spiritual successor" to Kino's Journey out there, it is Shigofumi. Each follows an observer and her inanimate partner through a variety of individual stories, most involving some sort of social commentary, irony, message, etc. It's worth noting that Shigofumi has more of an overarching plot than Kino, with a few recurring characters and a dedicated development of Fumika's backstory over time. Whether this is ultimately for the better or not is up to the individual, but in the end anyone who enjoyed one of these series should surely find the other to their liking as well.

Serial Experiments Lain and Shigofumi are different, but somehow Fumika did remind me of Lain, and also there seemed to be some similarity between supporting characters. There is also one theme that appears in both shows, but I don't want to spoil so I'm not telling what it is. If you liked one of those I can't guarantee that you're going to like the other, but you should check it out anyway.

In Perfect Blue we have Mimi, in Shigofumi we have Fumiko.. both suffer from tricking themselves into thinking that by doing something to please someone else they will be more loved, happier or just better off for it. Mimi has her agent, Fumiko her father. For both it ends up completely different and far from where they want to be or where they thought they were going. Truly I believe these 2 characters to be kindred spirits in their self imposed sufferage that they must attempt to overcome.