Can an owl turn its head all the way around? The answer can be yes or no, depending on the starting point of the head, so some clarification is required.
If the starting point of the head is facing straight forward, then no, they cannot turn their heads all the way around. If YOU start out facing forward and turn your head as far to the side as your head will go, most people can turn their heads about 90 degrees. An owl, however, can start out facing forward, turn its bill over its shoulder, keep going until its bill is over its spine, then keep going until the bill reaches the other shoulder...a whopping 270 degrees from the front!
That being said, you will almost never see an owl turn its head more than 180 degrees from the front. They almost always stop when their bill is over their spine and rotate their head around to the other side to continue watching something if necessary.
Now if your starting point for this whole head-turning discussion is with an owl's head over its spine, it can easily turn its head back the way it came from to the front, then all the way to the spine in the other direction, making for a nice easy 360, something they do regularly. So if your starting point is to the rear, then yes an owl can turn its head all the way around.
Now to get the idea of the absolute extremes of which an owl is capable, if an owl starts with its head at the maxium twist of 270 degrees (from the front), then goes back to the front and does a maximum rotation in the other direction, the full range of motion is a whopping 540 degrees! (Never mind that you'll probably never see an owl do more than the 360 described in the previous paragrah.) A human's maximum range of rotation from side to side is more like a measly 180 degrees.
Here's a rare video of an owl acutally rotating its head a full 270 degrees from the front.
Below is a video that shows the adaptations owls have to allow them to turn their heads so far. (Note that the video of owl head-turning in this video doesn't show an owl turning its head 270 from the front--even the video makers didn't grasp the concept of what it means for an owl to turn its head 270 degrees from the front!)
So now you know the whole answer....