Rammed earth is good; look to the work of Rick Joy, one of my favourite architects over-all, and the best use of rammed earth I've seen.
Another similar but different method is Cob - I don't rate it highly, it's not bonny, generally only used in areas where it was the vernacular at one time.
Again adobe (no not Adobe) is a bit crude, and not great for walls, but an adobe and linseed oil floor can be a pretty cool thing.
Straw bale architecture is good, sound absorbing - both high and low frequency, highly insulating - mostly due to its thickness, fire retardant - a lime rendered wall = F120, what's not to love? Dimensional stability isn't great, poor detailing leads to damp, leads to rot, leads to...
Modular post and beam timber, look to Glenn Murcutt.
And etcetera, and etcetera, and etcetera.