This is funny in that I'm looking down this is list of recommendations and just about every one of them have parts related to Japanese concepts of spirits/demons, which is something the original poster was asking advice how to avoid. For example:
* Dragonball Z, Fist Of The North Star, most martial arts based animes - They're always developing their Ki. What's Ki? Spiritual power. (Also, in Dragonball Z at least, they regularly visit the spirit world in several episodes, which is occupied by spirits and demons.)
* Death Note - An anime about a note with great spiritual power that is used to direct demons to kill people.
* Baccano - A story about immortality serum granted by a demon.
* Clannad - While mostly a slice-of-life anime (and absolutely awesome show), the supernatural factors heavily into the undertones of this show.
* Akira - This one's a bit dicey. While not a demon per se, but Akira has a lot of happenings heavily inspired by demons, and the espers psychic powers can be seen as spiritual.
And so on. That said, there has been a few recommendations which passed this criteria, for example:
* Gundam - I'm pretty sure that, aside from maybe the name of some of the characters/gundams, there's no demons or spirits here.
* Cowboy Beebop - Mostly straight up Sci-Fi, though there's a few episodes involving characters who utilize spiritual tricks. Spike's Native American consul, for example.
* Ouran High School Host Club - Pretty much zero spirits and demons here, although the concept of a "host club" is somewhat Japanese, and sometimes they dress up in traditional Japanese outfits, and then there's that guy who believes in black magic...
* Ghost In The Shell - Pretty much straight up Sci-Fi involving the concepts of cyborgs.
