Loxodromes
From Vectorcalcumb
So, here is a link to an animation of a Loxodrome drawn on a sphere: http://www.owlnet.rice.edu/~fjones/loxo.html
Also, note that if you just go to: http://www.owlnet.rice.edu/~fjones, the guy has written a book on vector calculus that he makes available for free.