Using the Spitzer space telescope, astronomers have observed that binary (or twin) star systems are just as likely to have planets around them as single star systems (like our own). In fact, some evidence points to planetary systems being more common around tight binary pairs than around single stars (with a possible ratio of 3:1).
A tight binary is where each star circles the other closely, say within 3 A.U.s or closer. A planet in the habitable zone of that system would see double sunsets like what the fictional Luke Skywalker saw on his home planet of Tatooine. The stars could be double gods, twin gods, to a developing sentient culture; though the comments about the trinary system come into play here as well: sentient beings on desert planets may hold water to be a higher deity, or at least the good deity, and sentient beings on water planets may, depending upon environmental conditions, hold underwater volcanoes or volcanic vents to be a higher deity, with the sky an alien, otherworldly place (maybe the afterlife - or hell).
Wide binary systems would have sunsets similar to our own on Earth - the second star would be so far away as to barely interact with the main star and the planets circling it. Sunsets there would have one large sun setting, with the second sun appearing as a bright star. The bright star may hold a place in developing primitive theologies, but, baring other factors (large nearby galaxy visible in the night sky, orbiting a large gas giant that may block the night sky half the time, or if the habitable moon is in phase lock with the gas giant, the sentient beings nocturnal, to name a few), the main star would be the center point.
I suppose it is a small possibility that in some systems the far off twin could have planets about it. What an interesting system that could be if life arose on planets circling each star - each unaware of the other until technological developments allowed one, or both, to spot the other. It would still be quite the feat for each planet to physically visit each other, not until space travel more advanced than what we have now is developed; but at first tentative long range observations, then electronic communication and space probes could establish some kind of communication between the two. What kind of theologies would exist there?
And what would happen for two planetary civilizations to be that "close" to each other to come in contact with each other versus two planetary civilizations from totally different solar systems, separated by much more distance (and thus slower communication, and less likelihood of physical contact). Probably easier to keep such a thing secret from the public, but in a wide binary system, the other civilization would be easier to detect and communicate with, thus making it harder to keep the existence of another civilization secret - not without going through extreme measures like banning all public ownership of telescopes, both optic and radio, and, if they have a planet of sovereign nations, or similar social structures, that would add another layer of difficulty in keeping the other extraplanetary civilization secret.
"Alien Sunset." Spitzer - NASA. 29 March 2006. 22 November 2007. <http://www.nasa.gov/mission_pages/spitzer/multimedia/doublesunset.html>.
"NASA Telescope Finds Planets Thrive Around Stellar Twins." Spitzer - NASA. 29 March 2006. 22 November 2007. <http://www.nasa.gov/mission_pages/spitzer/news/spitzer-20070329.html>.
From Digital Blasphemy <http://www.digitalblasphemy.com/>.