Although aikido isn't a religion, I think it definitely is a way of life - which may blur the lines a little.
For me, I find Zen, with its practice of Zazen meditation and generally non contending philosophy to fit right in with Aikido, and helps me a lot. Since I've started doing 25 minutes of zazen before each practice, I've felt much more peaceful on the mat.
Another thing that helps - is Taoism, which is conveniently mixed into zen. If I ever need to chill out, and training isn't an option, and I don't feel like zazen - then reading the Tao Te Ching does the trick. I'm going to quote my favourite passage from the Tao Te Ching, which I believe is very "Aikido," and is what I try to live by:
Best to be like water,
Which benefits the ten thousand things
And does not contend.
It pools where humans disdain to dwell,
Close to the Tao.
Live in a good place.
Keep your mind deep.
Treat others well.
Stand by your word.
Make fair rules.
Do the right thing.
Work when it's time.
Only do not contend,
And you will not go wrong.
-Tao Te Ching, chapter 8. Translated by Stephen Addiss and Stanley Lombardo, with an opening by Burton Watson. Originally written by Lao Tzu.