Ah, I see! Cair is the first -air verb I've encountered. The grammar I've read talked about -ar, -er, and -ir verbs. I assumed Cair was irregular. It's good to know dozens of other verbs conjugate the same.
I have a background in Latin, so most of the irregular verbs don't surprise me. Ser seems to make more sense than Latin's esse :)
This is strange. I just found a site that lists Cair as irregular. http://www.portugueselanguageguide.com/languagetools/portugueseverb.asp
I really need a good Brazilian Portuguese grammar book for reference. My dictionary is in the mail. I hope it has some grammar tables :/