There aren't really, from what I know, any thresholds of transportation between worlds that would resemble portals in modern fantasy. Like all modern fantasy, however, such concepts of portals arise from myths.
A prominent symbol of travel between worlds is the river. Cultures stemming from Indo-European language groups hold this mythological motif in common. A soul must pass across a river to reach the afterlife, often with the help of a ferryman (see Charon, Urshanabi, and otherworlds like Avalon), or be guided to the next life by a psychopomp. Mist and birds carrying or embodying human souls are prevalent in these instances.
As for specific portals, the Bifrost in Norse myth is more of a pathway than a portal, as are most thresholds that link worlds in mythology. However, some portal-like concepts exist, such as the fairy rings of European folklore and the sidhe mounds of Celtic myth. Again, myths of specific portals are sparse. Gates in mythology are fairly common, but they typically have a more symbolic purpose, like the Egyptian gates in the Duat and the Christian gates to Heaven.
Actually, this is likely more along the lines of what you're looking for. The ancient Hebrew text, The Book of Enoch, makes explicit references of many portals between the heavenly and mortal realms, probably as a primitive explanation of how celestial and meteorological forces affect our world. This particular passage in The Book of Enoch, from Chapter LXXII of The Book of the Courses of the Heavenly Luminaries, is an example of these portals frequently mentioned in the text. In this case, an explanation of celestial bodies traveling across the sky:
And this is the first law of the luminaries: the luminary the Sun has its rising in the eastern portals of the heaven, and its setting in the western portals of the heaven. And I saw six portals in which the sun rises, and six portals in which the sun sets and the moon rises and sets in these portals, and the leaders of the stars and those whom they lead: six in the east and six in the west, and all following each other in accurately corresponding order: also many windows to the right and left of these portals.