Absolutely! Sometimes those are the most interesting results.
There have been a few times when I've looked at the data and expected to see one thing and saw something very different. Generally this is a sign that we don't completely understand the physics at work. But it also means another clue into unraveling the puzzle.

Almost every time we've looked more closely at a phenomenon, whether with more sensitive instruments or from a different physical position (closer or off to the side and away from Earth, etc) or using a different type of observation (for example a different wavelength of light) we find something unexpected. Generally things like the Sun or the space around the Earth are much more complicated than they initially seem. While it can be frustrating at times, it is also what makes studying these things so interesting.

All the time! One of the clearest examples from my experience was when one of our sounding rocket instruments experienced a failure during flight. There was a short in a wire sending power to the camera shutter, so it didn't open as expected and we just got a lot of images of the back of the shutter instead of the sun! Talk about disappointing! But fortunately, we were able to re-fly within the following year and the next flight was very successful....