I'd have to say that my favorite part of myself is most deffinately my hair. It's extremely long (not to mention a pain in the a** to keep up, but I love it anyway) and it's taking a lot of beating for it to be in the healthy shape that its in. At this point, it reaches to about mid-butt.
As for a least favorite part...that'd have to be my legs and/or upper arms. I had a bad fall years back that left some scars on my legs that are less than attractive. Cancer invading the muscles in my upper arms, and the surgery that followed, had the same effect.