Here are a few things of interest, of course there are many more:
1. They invented the representative form of government known as a republic, as opposed to participatory democracy a la the Athenians. We live in a republic.
2. Justinian’s Code and other Roman law was a basis for European legal systems until largely modified by Napoleon’s Code. You’d be interested to know that Code law (as opposed to the common law) was the basis of law in originally French Louisiana.
3. The system of dioceses and officials running them was adopted by the early Roman church, and still exists.
4. They invented the pipe organ.
5. We still use the Roman alphabet.
6. The Roman calendar was still in use until about the 18th Century (I think that was around the time it was switched).
7. The Romans were into cleanliness, and had bath houses for the public.
8. The Romans invented plumbing, and even invented the valve for use with it.
9. The Romans had heated flooring in places like bathhouses.Unfortunately, you wouldn’t have wanted to be a slave making sure the heat was working underneath the flooring, but you know..
10. They had perhaps the first professional laundries.
11. Rome invented the shopping mall, and Rome had a huge three or four story one (Trajan’s Market).
12. Most ordinary Romans didn’t often cook in their apartments (that were multi-story, though they didn’t invent the apartment); they ate at street cafes.
13. Roman legions had running water in their latrines, and cleaned themselves after doing their business.
14. Roman medicine wasn’t surpassed until after the American Civil War. They could operate on cataracts, invented the use of sutures, knew about poppy derivatives for anaesthesia, had primitive antiseptics even though they didn’t understand germs, knew about various herbal remedies, were the first to use dissection to understand how the human body actually worked, etc., etc. A Roman soldier was more likely to survive a wound than a Civil War soldier. Think about that!
15. By the third century AD, Roman cavalry adopted the heavily armored cataphract idea from the Parthians, and improved on it, creating plate armor, etc. The Romans also used chain mail before the time of Caesar. The cataphract was the ancient world’s human tank.
16. Roman legions invented the idea of the salary, so called because the soldiers were partially paid in salt (salarium). Salt was valuable.
17. The Romans built paved roads all over Europe, so that their armies could move freely. Their roads were so solidly built that some have lasted until the present day. They invented a machine to measure mileage where a wheel turned a gear, and the gear spilled a little ball into a basket after intervals of one mile (which was mille passum, or 1000 paces). Mile markers were erected to show distances.
18. They invented concrete that could solidify under water to build piers and docks. And the dome, and probably the curved arch, as opposed to post-and-lintel.
19. Roman basilicas were large, multistory public buildings that had courtrooms and other government facilities that would look familiar to us. And some had stores and shops on the ground floor. So yeah, if you want to blame ‘city hall’ on someone, blame those guys!
20. They invented the true stadium, which is in itself a Latin word, and not only that, the Coliseum in Rome had a retractable canvas roof over the stands that could be used to shield them from the sun and rain. They held re-creations of sea battles in the Coliseum - this was once doubted by historians, until during the 20th Century, they found the actual plumbing pipes that brought in the water!
21. They also did a bunch of stupid stuff. Everyone does.
I could probably think of other things, but I have to actually work today at some point!