Yes, it's difficult to find something unique to Romans, because it had been invented by cultures before them, but they were able to expand it and they contributed to many aspects of life - politics, law, architecture, medicine, military... (they somewhat lacked in philosophy or mathematics, but I would say that they just liked practical things that could have been used immediately). Yes, Greeks had that, Celts had that, Etruscans had that, but Romans had all of it and better!

And by joining many nations and cultures under their rule and taking their best, they formed predecessor of common western culture. Something that Alexander and Diadochi wanted, but did not manage. That's why todays high school students learn about Alexander and Diadochi at one lecture and about Rome for months (at least I did).

But I still like Greeks and Celts more and I am a member of Romaioktonoi group.