If luck is on your side, you can see marmoset monkeys at Urca Hill (in fact they can be seen in different areas in Rio de Janeiro).
Feeding the monkeys is not allowed (it might be because some tourists give them cookies or other synthetically produced food items, which are not at all part of their natural diet).
Besides monkeys, you can see birds as well as lots of lizards (you can spot them right after the safety barriers, when you overlook the bay).
See here photos of both: Sugar Loaf and Christ the Redeemer statue atop Corcovado Mountain