As my colleague Pinkfreud notes below, Orangutans are apes rather than monkeys.
The Smithsonian's National Zoo's web site has excellent information
about the differences between apes and monkeys.
Differences Among Prosimians, Monkeys and Apes
As indicated on those web pages, apes do not have tails while most
monkeys do have tails. There are exceptions, though, such as the
North African macaque which is a monkey that has no tail.
Generally, though, monkeys have tails. However, not all monkeys have
"grasping" (or "prehensile") tails used like a fifth limb for swinging
from tree branches or grabbing things. You mentioned spider monkey.
Spider monkeys have "prehensile" tails. Other monkeys such as baboons
have tails but they are not prehensile.
The difference here is geographic. The monkeys with prehensile tails,
such as the spider monkey, are native to South America (and Central
America) and are considered "New World" monkeys. "Old World" monkeys
in Africa and Asia never have fully prehensile tails.
Why the difference? Well, scientists point out that the prehensile
tail is a useful adaptation for the life in the trees enjoyed by the
monkeys of the tropical rain forests of Central and South America. By
comparison, "Old World" monkeys in Africa and Asia are more
"terrestrial" (i.e., they operate at least some of the time on the
See Singapore Zoo Docent:
"NEW WORLD MONKEYS
Unlike their Old World counterparts, these monkeys are superbly
adapted to an exclusively high life in the treetops. Living at such
heights, they feed almost entirely on leaves and fruit. An arboreal
existence is less complicated than life on the ground. There is ample
food and few large predators, aside from larger snakes and some of
birds of prey.
... They have long-raking limbs and some have prehensile tails...
OLD WORLD MONKEYS
The largest and most varied group of primates, Old World monkeys, are
adapted to a more terrestrial lifestyle. They all spend some time on
the ground and are predominantly omnivorous, eating mostly plants.
Unlike the New World monkeys, they are not restricted to tropical and
sub-tropical forests, although that is where most of them occur. They
live in virtually every kind of habitat there is on land - from
treetops to grasslands and cliffs...
...They have a tail, which may be long or vestigial, but is never
fully prehensile as in cebids. All of them walk and run on their hands
and feet. Even the ones that live in trees run along the tops of
branches; they never swing along underneath them like spider monkeys."
Singapore Zoo Docent: Cebidae
The Primates: New World Monkeys
zoo, "between monkeys and apes"
prehensile tail monkeys
I hope this helps.