Digimon Tamers, Devil Survivor 2 The Animation Recommendations
Believe it or not, Devil Survivor 2 and Digimon Tamers are probably the closest anime in terms of similar themes you'll find.
In both of the shows, creatures are appearing out of no where in Japan and causing havoc. In DS2, the ones who take care of these are the summoners, while in DT they are the tamers. In DS2 they use a variation of demons from folklore, stories and the such, while in Digimon Tamer it gets to the point where the enemies are based on folklore and legends as well. In DS2, you can almost consider the demons to be 'digital' as well as
In essence, there exists supernatural beings that are from another world/dimension that threatens the people that resides in their respective series. These beings have their special abilities.
Some of the people from both series have partners/summonings of their own and are able to combat these beings.
The main male protagonist from both series strives to make the most of his life and with his partner often tries to help others along with his friends. There is also action, drama, and other strange supernatural phenomenon going on in both series.
Both are about kids that fight against monsters who are a menace to the world controlling other monsters. The story gets pretty dark very quickly. The organizations who intervene in the story, the JPs (Devil Survivor) and Hypnos (Digimon), are very similar. Some of the monsters of both series are based on mythology.
Three ordinary kids, two boys and one girl, that all of a sudden have mysterious beasts that they can control and use to fight other mysterious beasts in order to protect their city. Not to mention just the overall feel of it. I would say that Devil Survivor 2 is more mature, but that's about it.