The obvious differences between the universal use of tools by humans and their sparse use by NHPs suggests understanding tool use may reveal much about human nature and its origins.
Despite such ignorant suggestions to the contrary, tool use in NHPs has been known at least since Darwin. He noted, for example,:
It has often been said that no animal uses any tool; but the chimpanzee in a state of nature cracks a native fruit, somewhat like a walnut, with a stone.  Rengger  easily taught an American monkey thus to break open hard palm-nuts; and afterwards of its own accord, it used stones to open other kinds of nuts, as well as boxes. It thus also removed the soft rind of fruit that had a disagreeable flavour. Another monkey was taught to open the lid of a large box with a stick, and afterwards it used the stick as a lever to move heavy bodies; and I have myself seen a young orang put a stick into a crevice, slip his hand to the other end, and use it in the proper manner as a lever. The tamed elephants in India are well known to break off branches of trees and use them to drive away the flies; and this same act has been observed in an elephant in a state of nature.  I have seen a young orang, when she thought she was going to be whipped, cover and protect herself with a blanket or straw. In these several cases stones and sticks were employed as implements; but they are likewise used as weapons. Brehm  states, on the authority of the well-known traveller Schimper, that in Abyssinia when the baboons belonging to one species (C. gelada) descend in troops from the mountains to plunder the fields, they sometimes encounter troops of another species (C. hamadryas), and then a fight ensues. The Geladas roll down great stones, which the Hamadryas try to avoid, and then both species, making a great uproar, rush furiously against each other. Brehm, when, accompanying the Duke of Coburg-Gotha, aided in an attack with firearms on a troop of baboons in the pass of Mensa in Abyssinia. The baboons in return rolled so many stones down the mountain, some as large as a man's head, that the attackers had to beat a hasty retreat; and the pass was actually closed for a time against the caravan. It deserves notice that these baboons thus acted in concert. Mr. Wallace  on three occasions saw female orangs, accompanied by their young, "breaking off branches and the great spiny fruit of the Durian tree, with every appearance of rage; causing such a shower of missiles as effectually kept us from approaching too near the tree." As I have repeatedly seen, a chimpanzee will throw any object at hand at a person who offends him; and the before-mentioned baboon at the Cape of Good Hope prepared mud for the purpose.
In the Zoological Gardens, a monkey, which had weak teeth, used to break open nuts with a stone; and I was assured by the keepers that after using the stone, he hid it in the straw, and would not let any other monkey touch it. Here, then, we have the idea of property; but this idea is common to every dog with a bone, and to most or all birds with their nests.
The Duke of Argyll  remarks, that the fashioning of an implement for a special purpose is absolutely peculiar to man; and he considers that this forms an immeasurable gulf between him and the brutes. This is no doubt a very important distinction; but there appears to me much truth in Sir J. Lubbock's suggestion,  that when primeval man first used flintstones for any purpose, he would have accidentally splintered them, and would then have used the sharp fragments. From this step it would be a small one to break the flints on purpose, and not a very wide step to fashion them rudely. This latter advance, however, may have taken long ages, if we may judge by the immense interval of time which elapsed before the men of the neolithic period took to grinding and polishing their stone tools. In breaking the flints, as Sir J. Lubbock likewise remarks, sparks would have been emitted, and in grinding them heat would have been evolved: thus the two usual methods of "obtaining fire may have originated." The nature of fire would have been known in the many volcanic regions where lava occasionally flows through forests. The anthropomorphous apes, guided probably by instinct, build for themselves temporary platforms; but as many instincts are largely controlled by reason, the simpler ones, such as this of building a platform, might readily pass into a voluntary and conscious act. The orang is known to cover itself at night with the leaves of the Pandanus; and Brehm states that one of his baboons used to protect itself from the heat of the sun by throwing a straw-mat over its head. In these several habits, we probably see the first steps towards some of the simpler arts, such as rude architecture and dress, as they arose amongst the early progenitors of man.
(Descent of Man,1871, Ch.III)
Some of the earliest experimental work including that of Kohler and others documented considerable tool-using capability in the laboratory, supplementing the anecdotal observations from performing apes and early naturalistic observations (Garner, 189x).
Recent research --Goodall's observations on chimpanzees' use of sticks in ant fishing, detailed accounts of nut-cracking-- as well as experimental work demonstrate and more imortantly refine both the degree and limitations of tool-use in NHPs. This research does not radically change our conception of the primate order--except perhaps for those who were ignorant of prior work.
The more sophisticated recent analysis, do however, raise subtle and important questions about how individuals and social groups come to utililize tools.
Bryne says: "single, isolated cases of object manipulation give little confidence that the perpetrators have a general understanding of cause and effect relations among objects; a wider repertoire of tool use, showing some flexibilty, would point more clearly to intelligent usage....for a few species of primates....a picture of animals that can use a range of tools for a range of purposes, animals that can choose between methods. This suggests real intelligence 88-9."
Also see Nagell, K., Olguin, R. S., & Tomasello, M. (1993). Processes of social learning in the tool use of chimpanzees (Pan troglydytes) and human children (Homo sapiens). Journal of Comparative Psychology, 107, 174-186. (video data)
"I believe these studies suggest that chimpanzees and human children understand the tool-using behavior of conspecifics in different ways. For human children, the goal or intention of the demonstrator is a central part of what they perceive and, thus, her actual methods of tool use--the details of the way she is attempting to accomplish that goal become salient. For chimpanzees, the tool, the food, and their physical relation are salient; the intentional states of tahe demonstrator and her preceise methods, on the other hand, are either not perceived or seem less relevant. p. 305"
Synergy with brain size, lateralization, and hand took over several million years.
Recent research suggests, somewhat controversially that even "Lucy" used tools to cut meat (video) (http://www.youtube.com/watch?v=V2YMfzhm8ao). Also see these supposed 3.4 mya australopithecus tools found in Ethiopia.
Annett (19xx, 1991) has argued handedness is a genetic trait related to language.
MacNeilage (19xx) argues in his "postural origins" theory that handedness has its roots back in ancient prosimians who clung to branches with their right hand and reached for food with the left. One implication from this theory is that to really evaluate handedness, the animal has to be put in certain situation for a handedness tendency to reveal itself.
Overall species, there appear to be three general tendencies. The prosimians, like their ancestors, still display a left hand preference. whereas apes in varying degrees and situations and of course humans , prefer their right hand. In m
McGrew and Merchant, 1992, for example found no handedness in termite fishing but a right hand bias in reaching. Hopkins, Bard, Jones, and Bales, 1993 found an interesting relationship between throwing hand, position, and sex. Captive females were more likely to throw with the right hand in both four and two legged positions; while males used their right side much more when bipedal.
This raises some interesting speculation about the possible interrelationship of human lateralized function, language, and bipedality.