One of the most intriguing objects that we have photographed with the Hubble telescope is the "Red Rectangle." This object is a very unusually-shaped nebula.
The star in the center is one (or maybe two, we now think) very similar to our own Sun. It has reached the end period of its life and is now ejecting material from its outer layers. Why it looks like this (the color and structure) is still something of a mystery. Don't you just love a mystery?
Of course I say "one of the most intriguing objects" because Hubble has photographed so many amazing things! I really hope we can keep it going.
Photo credit: NASA; ESA; Hans Van Winckel (Catholic University of Leuven, Belgium); and Martin Cohen (University of California, Berkeley)
(by the way, the above image was gleaned from http://hubblesite.org/ they have a lot of other great images to check out)