My offering into the James Maliszewski call to share what we've done with these critters to make them our own.
The one monster I changed the most was the Goblin. These guys have as many depictions as any monster, from the vicious minions of Saruman, in the Lord of the Rings to the Dobby in Harry Potter. I know Dogby is described as a house elf, but you know and I know he's a goblin. *see comment with Sean about the banker goblins*
The goblins in my campaign are a cultureless race. They have no god they collectively worship. They have no customs or traditions they carry on from generation to generation. They are a blank slate. But masters of imitation. Goblins search for another race to learn from. Goblins will worship the same god and celebrate the same holidays and social occasions. They will build a shanty town near the other race's settlement and it will imitate the village or town's layout.
The imitation is never quite correct and often comical in its execution. Goblins will take up the worship of local gods, but often will change the name that is more familiar with their language. They will also create mock up of the refined wear priests and acolytes wear. If your religion requires the acolytes to wear a plain brown robe you can be sure you'll be seeing a group of acolyte goblins donning burlap bags or potato sacks. Though they may miss the mark with their imitation, Goblins are very respectful and honor the local gods.
Though not many races like having goblins around underfoot, they are very useful. Goblins are also masters of salvaging. When a goblin settlement is nearby the sanitation increases because the goblins go through all that is tossed out, organize it and use what they can destroy the rest. Large cities usually have a goblin settlement nearby so their 'city dump' doesn't become a problem. The goblins also keep the rat population down. Goblins hunt the rats for food. The other benefit of having goblins nearby is they are a source of cheap labor and never complain about doing the horrible jobs. Most large cities employ several teams of goblins to keep the sewers clear.
On very rare occasions when a goblin community is being abused or systematically slaughtered the community as a whole can go into 'goblin rage'. When a goblin community final enters goblin rage they have gone feral and will attack any living thing with a berserker rage. These are the wild goblins adventurers encounter in the wilderness. They live to kill at this point and nothing more. Should a goblin infected with goblin rage enter a docile goblin community, the rage will spread and within a few hours all goblins within the community will be infected. No alchemical or magical solution has been found to cure goblin rage.
As a whole, goblins a passive race, but once in a great while an extraordinary goblin will rise above his peers and make a significant contribution; some have become elders in their church, some hold minor positions in the local government and a more than a few have become successful merchants. Although they may never be generals or bishops or kings, goblins do not dream of power they are motivated by learning. Though they are limited with what they learn they never stop trying to become better. They also are protective of the friends they make and have been known to sacrifice themselves to aid the hosting community.