I always enjoy seeing turtles when diving and have been lucky enough to see quite a lot although they are far from common. Turtles are the classic example of a species divers often see disappearing into the distance and rarely close up. I've found that if you respect their space and don't make them feel trapped or threatened you can get a nice close look (and the chance of some decent photos). This is a hawksbill: This may be a misconception based on my personal experience but I've always seen hawksbills as kind of greedy - check out this guy:
Green turtles by contrast I think of as the chilled out surfer dudes like in Finding Nemo. This one was chilling on the seagrass with his remora friend and about 8 other huge turtles.
I'm not usually a big one for anthromorphising but turtles seem to bring this out in me for some reason.