This is a great question. The Romans created so many thing that it will be difficult to limit my answer. In light of this, let me name three great achievements.
First, the Romans were masters of statecraft. Therefore, their empire was one of the largest in the history of the world. They possessed land from modern day England to North Africa to Central Asia. They were able to do this, because they had amazing governmental structures in place. The Roman constitution was an impressive framework for governing.
Second, the Romans were experts in engineering. Their roads, buildings, and aqueducts were nothing short of amazing. Even today, Roman roads and bridges are in use! Some aqueducts were over 100 miles long. If we gaze at their buildings, they were equally impressive. Think of the Colosseum in Rome.
Finally and arguably most importantly, the Romans gave us their body of law. Justinian, the Emperor, codified Roman law and this passed into Medieval Europe and from there to many other places. Roman law was one of the most important contributions to the world.