A fun way to mount art is to float it between glass. A "glass float mount" is a mounting process in which a flat art piece is sandwiched between two pieces of glass. This generally means no adhesives, the art is held in place by the weight of the glass.
The frame can be place right next to the boarder of the art, however, by spacing the art away from the frame and cutting the glass larger than the art the raw edge of the art can be seen. This process is commonly used on papyrus, watercolors, pressed flowers, and fabric prints, but can be used for other art pieces.