I am curious as to the species or "types" of archaea that have been found to reside within animals symbiotically. One of the only ones I can think of off the top of my head are methanogens, which live in the gut of ruminants for example.
A pioneering study using 16S RNA primers found only Methanobrevibacter smithii in the human intestine.
In a recent review there is a comprehensive Table of archaea found in humans (this includes non-intestinal flora):
Much of the work that is catalogued by Dridi et al. is repeated identifications of Methanobacteriales (Methanobrevibacter smithii, Methanosphaera stadtmanae and Methanobrevibacter oralis), but there are others from the Thermoplasmateles, the Halobacteriales and the Sulfolobales, plus some that are thought to be members of unknown archaeal orders.