High Seas has warforged originally designed for mining operations deep beneath the ocean, what with not needing to breathe and all.
The idea of warforged being used only for war has always struck me as a little silly: a sapient being is so much more versatile than that. It makes more sense to put the "war" part of the name from your mind, and think of them as robots like any other robots.
Which is to say, basically, this: think of a thing that's too dangerous or too low-oxygen or gross or tedious for feeble normal fleshy people to do; somebody made a line of warforged to do that thing.
Specific ideas to play with:
- undersea exploration/work
- space exploration/work
- exploration/work on hostile planes
- mining of any sort
- sewage treatment and sewer line maintenance
- household chores
- guinea pig (specifically thinking "test pilot", however you might go about incorporating that concept into D&D)
- research ("Librarian-bot, find me all the information you can on avocados...")
- law enforcement (or traffic enforcement)
- worshipping a deity to free up the rest of the community for more useful activities (along the lines of prayer wheels, the Tibetan devices which do your praying for you)
- worshipping a deity because the deity in question is such a distasteful one that you're trying to power it up with prayer but wouldn't be able to find very many human worshippers to do it
(Side note: most of those are pretty good if I do say so myself, but holy awesome those last two are an amazing idea and I must immediately incorporate them into my campaign setting.)
On another side of the d20 altogether, for an individual adventurer rather than an entire line of them: the notion of a warforged who broke free of his creators and is now his own guy is probably Drizz't-level cliche at this point, but there are still drastic variations on that which aren't common in D&D.
I'm thinking specifically this: (re)read I, Robot and the rest of Isaac Asimov's robot oeuvre, most of which take the form of logic puzzles or detailed explorations of a concept, where the concept is almost always a variation on "Robot X is Three Laws safe in every way, except for subtle defect Y" ("It can read minds"; "it's missing the 'or through inaction' part of the First Law"; "it's put into a situation where the laws conflict in exactly the wrong way"; "it has creativity").
I mention Asimov only because he put out the highest volume of the purest distillations of this trope. You could also consider things like Data, Marvin, or Kryten; basically any fiction that has a robot. Or just pick a random robot trope. There's such a wide variety of fiction to rip off, it's hard to know where to start!