I think the biggest issue in this topic is that certain people feel that the non-human races in D&D need to be X amount different and Y amount flamboyant about it. It's the "If I forget your player is a non-human for five seconds while your talking..." mindset. The reality is, people play the stereotypes when they play dwarves and elves because few people have tried to delve into the psychology of an imaginary species to a depth of a virtual awakening of an elvish mind in their consciousness, and it's never going to happen. Even if a player were to read every book ever written with an Elvish narrative he's going to get conflicting views, cultures, customs and habits. Which means s/he's going to wind up having to sort through a million thoughts about what an Elf should be.
I play a lot of dwarves, occasionally elves, sometimes halflings. Do my characters exhibit stereotypical behaviours? Yes. Do they have stereotypical names? Most of the time. Do they each have a well thought out background that drastically affects their perception of the world and makes them interact with each individual race differently? YES! Does that same background make them distinguishable from the rest of their own race? YES!
I think that we are forgetting that these character's we play whether they are human or non-human are supposed to be Extra-ordinary, they are not supposed to be like the rest of humanity, they are a special class, they have been selected for a life of super-human, super-dwarven, super-elven deeds that make them legends in the eyes of all races. Which means each character should also be differentiated from his or her own race, they are a step above. Maybe that means that after adventuring with some maniac's of other racial origins for a while they start to express and adapt some of the features of that character's racial background that he admires.
Let's say there's a party composed of two humans, a dwarf and a halfling. Let's start them all off with their perscribed game-fluff for a culture and suggested psychological traits. The humans would likely come to respect the dwarf's hard work, and would try to not falter in keeping up with him, the dwarf would probably come to admire the speed that the humans use to decide their best path, and their joie de vivre. The halfling being very human would probably respect both parties in the aformentioned ways, but would take more from the Dwarf's love of crafting beautiful things and the willingness to go to any lengths to honor his word. The Dwarf and the Humans would probably learn from the halfling how to take the small comforts of life as a necessity to quality adventuring, and admire his crafty, clever nature. For their experiences together the entire party would evolve together, and behave like no other members of their races, instead taking on traits of their unit. As is what happens with military units, you are a blank chip when you enter the machine, you have smooth edges out of boot camp, and your unit, it's motto and the people who serve with you change you as a human being, and you become a member of that team in all that you do, and it remains with you for the rest of your life.