|Sandberg, Anders. 2014|
According to the article to which I will give a link below, written by an Anders Sandberg, (a much more way smarter person than I) a donut shaped planet, according to the laws of physics, could actually exist. But it's highly unlikely that it could form naturally and be stable. If it were formed, it would probably have been artificially made by some species that had 1. the technology to do it, 2. a lot of time to make really big, pretty things just for fun, and 3. not much practical sense. (But, heck. My ancestors built Stonehenge, just 'cause they could, so there ya go.) (Now that I'm thinking about it, Stonehenge was probably built for religious reasons. Maybe that could be what would motivate them! Oh boy! So much potential for fictional world-building!)
Anyway, it would have a pretty quick spin (that's why it could hold its donut shape) yet stuff would still stay down (folks wouldn't go flying off of the equator) but the gravity would not be the same all over the planet, either. It would be a bit less at the equators (the inside and outside one) and greater at the poles (the top and bottom of the donut).
Things would be significantly different also, depending on if the planet is tilted or not. If it's got a zero degree tilt, the poor middle part would never see the sun, and be constantly frozen. But if it had a tilt like our planet, the middle part would not see the sun in the spring and autumn, but would be exposed to the sun in the winter and summer.
There's more interesting stuff to consider, including what it would be like if such a planet had a moon, and it it orbited the planet, possibly through the hole in the middle.
Check out the article here! It's very interesting!