What are the most important achievements of Roman architecture and engineering?
There are at least two ways to look at this question.
We can ask what sorts of ideas and materials the Romans used and perfected in their architecture and engineering. Among those are standardization, the use of the arch, and concrete. All of these were very important in Rome and are important today. Some people say the Romans invented the arch, but they did not. They only used it more widely and more effectively than any previous people had. Perhaps the thing that was most different about Roman architecture and engineering (compared to contemporaries) was its standardization. Romans tended to build similar buidlings in similar ways so that various types of buildings are easily identified. This evokes our own rationalized and standardized world.
We can also ask which specific projects were Rome's greatest achievements. The Colosseum, of course, is one of the greatest given that it was a huge structure that has managed to survive to the present. Its roads were a major achievement that were very important to Rome's power. The same is true of its aqueducts.
Roman architecture continues to have a strong influence to this day, and like many aspects of Roman civilization and culture, is often referred to as "classical" in style. Common elements of Roman architecture include the presence of columns, the use of symmetry and order in design, and the presence of a very strong and aesthetically pleasing entrance to any structure. The use of symmetry, in which buildings contain perfectly balanced design elements (equal spacing of columns, doors and windows throughout the entire structure, for example), is what characterizes many famous examples of Roman archictecture, including the Parthenon and the Coliseum. The Roman "look" of a building is so strongly prevalent in architecture that often buildings contain facades that are Roman in appearance, even if the buildings themselves are not Roman in design. Such facades are sometimes called "follies," as when a family home contains enormous Roman columns in front, despite not needing them for support, in order to lend a sophisticated or imposing appearance.