As we have seen, the various races portrayed in Middle-earth each demonstrate very specific invariable characteristics. Where do humans fit in among the other races of Middle-Earth? Are humans a “good” race?
The main defining characteristic of humans is that they are free to shape their own destinies beyond what is set out in the Music of the Ainur, and humans are unique in that they are the only species in Middle-earth that has this freedom:
Therefore he willed that the hearts of Men should seek beyond the world and should find no rest therein; but they should have a virtue to shape their life, amid the powers and chances of the world, beyond the Music of the Ainur, which is as fate to all things else... (The Silmarillion, Of the Beginning of Days)
Naturally this means that humans are also free to be good or evil, but, as Iluvatar says of those who fall into evil, "these too in their time shall find that all that they do redounds at the end only to the glory of my work".
This freedom is also the cause of human mortality, which is discussed later in the same chapter, although the reason why mortality needs to be a consequence of it is not given.
The accepted answer explains that Men were given the ability to "shape their life" in a way that other people could not. A comment on that answer suggests that their choices were influenced by their environment. I agree with both those points. So how did it actually work out?
The awakening of Men
We are not told much about the awakening of Men (the stories of the First Age were written by the Eldar). The Silmarillion suggests that Morgoth attempted to influence them in their early days and that as a result "a darkness lay upon the hearts of Men"
But it was said afterwards among the Eldar that when Men awoke in Hildórien at the rising of the Sun the spies of Morgoth were watchful, and tidings were soon brought to him; and this seemed to him so great a matter that secretly under shadow he himself departed from Angband, and went forth into Middle-earth, leaving to Sauron the command of the War. Of his dealings with Men the Eldar indeed knew nothing, at that time, and learnt but little afterwards; but that a darkness lay upon the hearts of Men ...
The Silmarillion: Quenta Silmarillion, Chapter 17: Of the Coming of Men into the West
Page 141 (George Allen and Unwin 1977 hardback edition)
We know that at least three families of Men resisted Morgoth's influence and set out journeying west to escape "the darkness". When Bëor, the head of one of the families met Finrod Felagund on the eastern edge of Beleriand, his people had already been travelling for generations and he is not sure what the "darkness" is that they are fleeing from.
But when he questioned him concerning the arising of Men and their journeys, Bëor would say little; and indeed he knew little, for the fathers of his people had told few tales of their past and a silence had fallen upon their memory. 'A darkness lies behind us,' Bëor said; 'and we have turned our backs upon it, and we do not desire to return thither even in thought. Westwards our hearts have been turned, and we believe that there we shall find Light.'
Now Felagund learned from Bëor that there were many other Men of like mind who were also journeying westward. 'Others of my own kin have crossed the Mountains,' he said, 'and they are wandering not far away; and the Haladin, a people from whom we are sundered in speech, are still in the valleys on the eastern slopes, awaiting tidings before they venture further. There are yet other Men, whose tongue is more like to ours, with whom we have had dealings at times. They were before us on the westward march, but we passed them; for they are a numerous people, and yet keep together and move slowly, being all ruled by one chieftain whom they call Marach.'
The people of Bëor, the Haladin and people of Marach became the three houses of Elf-friends who fought alongside the Eldar against Morgoth. While they lived for a long time under the influence of the Eldar, I think it is significant that they originally made the choice to reject Morgoth on their own before they ever met the Eldar.
Other Men in the First Age
After the Edain, a second wave of Men reaches Beleriand.
It is told that at this time the Swarthy Men came first into Beleriand. Some were already secretly under the dominion of Morgoth, and came at his call; but not all, for the rumour of Beleriand, of its lands and waters, of its wars and riches, went now far and wide, and the wandering feet of Men were ever set westward in those days.
But Maedhros, knowing the weakness of the Noldor and the Edain, whereas the pits of Angband seemed to hold store inexhaustible and ever-renewed, made alliance with these new-come Men, and gave his friendship to the greatest of their chieftains, Bór and Ulfang. And Morgoth was well content; for this was as he had designed. The sons of Bór were Borlad, Borlach, and Borthand; and they followed Maedhros and Maglor, and cheated the hope of Morgoth, and were faithful. The sons of Ulfang the Black were Ulfast, and Ulwarth, and Uldor the accursed; and they followed Caranthir and swore allegiance to him, and proved faithless.
The Silmarillion: Quenta Silmarillion, Chapter 18: Of the Ruin of Beleriand and the Fall of Fingolfin
Page 157 (George Allen and Unwin 1977 hardback edition)
Of the two main families in this group, one supports the Eldar and the other pretends to but then betrays them.
The War of Wrath
In the final battle against Morgoth, the Elf-friends side with the Eldar, but most Men fight on the other side.
And such few as were left of the three houses of the Elf-friends, Fathers of Men, fought upon the part of the Valar; and they were avenged in those days for Baragund and Barahir, Galdor and Gundor, Huor and Húrin, and many others of their lords. But a great part of the sons of Men, whether of the people of Uldor or others new-come out of the east, marched with the Enemy; and the Elves do not forget it.
The Silmarillion: Quenta Silmarillion, Chapter 24: Of the Voyage of Eärendil and the War of Wrath
Page 251 (George Allen and Unwin 1977 hardback edition)
Second and Third Ages
After the First Age, we hear of men who are both good and evil. By this time, they have all been exposed to both good and evil influences, so it is hard to say to what extent they are influenced by their environment.
So, are Men a "good" race?
Clearly they can be "good" or "bad" and they have the ability to choose which they will be.
I think the stories of the First Age suggest that Men do indeed choose between good and evil, and they do not always choose to act in the way suggested by their environment. It does seem that the number who choose good over evil is a minority, although that minority had a significant influence on events.