As we know many native American tribes were kicked from their homes and forced to leave their cultures, beliefs and belongings behind. Luckily the white man didn't always get their way and some Native Americans still practice and believe in various religions that aren't the typical ones such as Christianity and Judaism.
As mentioned above, even though America prides itself on it's constitution which includes the freedom of religion it did persecute Native Americans for practising their spiritual and ritual oriented religions but today there is still about 9000 people still practising Native American religions. Native American religions include Bole-Maru, Dream dance, Drum etc. It is a very diverse construct but all the religions have similar spiritual rituals.
I would argue that these Native American religions are more 'American' than say Christianity which we all know is an extremely hyperbolic symbol of America for example to quote Grace's post the use of "In God We Trust". The reason I believe Native American religions are more American is that Christianity or Judaism is part of the United States, not America. Christianity and Judaism are not native to America but these religions and belief systems are.
Unfortunately though the persecution and degradation of Native American religions is still strong today, often people are making a mockery (usually unintentionally) which images (typically tattoos) such as this;
These native religions are in my eyes more American than Christianity, luckily they now have the freedom to be practised and protected by the constitution. It's about time 'Americans' began to open their minds to religions that stray away from conformity and began to embrace other cultures and ideas that aren't pounded into their heads by old, out-dated teachings of their colonial ancestors. This isn't to say they should convert but just be willing to accept religions such as these without the idea of "oh here they go howling at the moon again".
Image 1; http://www.spiritalk.net/images/wolf-moonwolf-moon-native-american.jpg
Image 2: http://www.bbc.co.uk/staticarchive/ea35012b67112d2997cf0b42c21e2b928e14e6e4.jpg