From a purely astronomical point of view, this is definitely possible. There's no reason why you couldn't have a slowly rotating planet at around the same distance from it's sun as Earth is (well any reasons that do exist are fairly theoretical so we can ignore them). That said, if the planet is similar to Earth and its sun is similar to ours, then you kind of have to have the same length year because the length of the year (ie how long it takes to orbit the star) depends only on the mass of the star and the distance from it. This is due to Kepler's Laws, which I have previously discussed here. If you made no changes to star/planet distance, the year length would have to be the same.
|Image nicked from Wiki here. The little red line |
represents the same point on the surface of
Mercury. The numbers are the order in which
the positions happen: 6, 1, 2 are night for
the red line and 3, 4, 5 are day, roughly.
However, if we're talking a planet as distant from the sun as Earth is, there's no danger of it becoming tidally locked in the sort of cosmological time frame we're currently living in. The time taken for the angular momentum between planet and star to be distributed into the tidally locked configuration takes longer the further apart they are (and the less massive when they're close enough). The Earth-moon system will eventually become more tidally locked: the moon already faces the same side towards us all the time, and eventually the same side of Earth will always point towards the moon.
But that's a bit of a tangent, back to planets with long days and nights. You could have a planet rotating as slowly/quickly as you like, but you should be mindful that the people living there would almost certainly have a way of distinguishing between sidereal and solar days. Ancient people on Earth already had this worked out (the difference between sidereal and solar days is why the stars move across the sky with the seasons).
|Uranus: almost completely sideways.|
Also, astronomical plausibility aside, I'm not convinced complicated life could naturally arise on a planet with a super-long day/night cycle, due to the long periods of boiling (day) and freezing (night). In terms of temperature-stability, probably only the twilight areas would be habitable. I suppose you could have migrating species (but that also has problems because in staying in permanent twilight they'd need sufficient landmasses connecting the two poles). Also, you'd probably get some sort of storms around the twilight zone, since the temperature would be in in a state of flux. I'm not an expert on atmospheres or meteorology, though, so that's a (-n educated) guess and I can't be too specific. But in short: our 24 hour days are what keeps Earth's temperature relatively temperate and suitable for life.
There's be fewer issues for microbial life to arise but I don't know that anything larger would be viable. Maybe at the poles: if the planet was slightly closer to its star than Earth is, there could be non-migratory life living near the poles and with a stable orbit and rotational period, it should survive. Since the non-polar regions wouldn't have naturally arising complex life, there could be with completely different ecosystems/forms of life at either pole with only something like microbial ancestors connecting them.