To me, Warforged offer several amazing possibilities for exploration of humanity and society. Consider:
-Warforged were created artificially to fight in the Last War. Now that the war is over, and the Treaty of Thronehold granted them freedom, they exist as not only a painful reminder of the horror of the Last War, but also a segment of the population that is hard to integrate. I was listening to a podcast from Radio Free Hommlet, and they mentioned Vietnam, and all the problems returning soldiers faced (to be fair, Japanese and German soldiers returning after WWII suffered from the same problems, and that was heart-rending to read about).
Just think about the emotions there. The most powerful, fear; earlier Eberron books mentioned "lurid" depictions of Warforged soldiers drenched in blood, mercilessly hacking down a foe shattered and broken by the unrelenting assault of these metal monstrosities. How many veterans had their units virtually wiped out in a fashion that can be called, "inhuman" by these blank-eyed monsters? How many veterans watched a pitiless steel tide of "their own" Warforged annihilate an enemy unit? Now, combine that with the fact that these things, which are clearly not human, can talk, act, and make decisions like a human. Remember, Warforged have +2 to intimidate for a reason.
This dichotomy is something that would be utterly terrifying for most people. How many people fear and hate Warforged simply for what they are? How many tavern owners will devolve into hysterics when a 'forged walks through their door? How about 'forged in Thrane or Karrnath, where they are still virtually slaves? How would, "Cannith's Trash" be treated by the rest of the people in that nation? Jeff LaSala's The Darkwood Mask has a scene where a 'forged is pelted by rocks thrown by Karrnathi children, and a brave one calls the 'forged "Cannith trash". Where do these children learn to hate like that?
A module, Whispers of the Vampire's Blade, insinuates that 'forged are seen by some as simply weapons to be checked at the door of some places. How widespread would that be?
Consider extending that to society as a whole, with warforged fitting in. "The war is over," people say, "why keep around unneeded weapons?" Khorvaire doesn't need war any more, so what is the point in keeping these killing machines? Also, what are they going to do for jobs? Menial labor? "DEY TOOK UR JERBS!", if you don't mind the South Park. Just look at this picture from Sharn: City of Towers, and dwell on it:
Now, let us extend this into the realm of the practical for us players. How would a warforged deal with all the hate directed towards them? Would s/he become a jaded bigot, despising all breathers? A monk, seeking redemption (a-la Omax in the Heirs of Ash trilogy)? A hermit? Perhaps it would seek revenge, and become a brigand? Embrace its "violent nature" and be a mercenary or bodyguard? Why not seek justice, and become a watch officer or an inquisitive? Maybe it would seek to create things instead of destroying them, and become a farmer or craftsman. Simply dealing with the world is a massive roleplaying challenge for a player of a Warforged.
The other challenge which i far prefer is to use the inhuman nature to explore humanity. This is somewhat a motif of sci-fi, where androids or robots are taught what it means to be human. Still, though, consider how a warforged would think and see things, and be baffled by them. Why are you loyal to a country? How can you believe in something that does not exist tangibly? Faith? The stereotypical 'forged in the Last War just followed orders; explore morals and ethics. Explore simple kindness; when a 'forged sees a party member throw some jink (money) into a beggar's bowl, or gives some food to starving children, what does the warforged think about giving away supplies to non-mission-essential personnel? Ok, so that might be a tad too military, but still consider it.
To finish my overlong diatribe here, a Warforged offers very interesting roleplay possibilities that allow you not only to develop a character, but also explore what makes you human.