Architecture
The Romans were great engineers and builders. Many of their techniques have been used in buildings ever since. They invented concrete to make their buildings more durable. They used round arches and pillars to hold up large ceilings and built huge domes on their temples. Many Roman buildings were so well built that they are still standing today, like the Pantheon in Rome.
Christianity
The fact that the Roman empire became Christian meant that the Catholic Church became the world's most powerful religion in the following centuries.
Language
Latin was the language of the Roman empire. It is not spoken today, but many modern European languages such as French, Spanish, Romanian and Italian are based on it. English is not related to Latin but almost a quarter of English words are directly influenced by Latin.
Calendar
In 45 BC, Julius Caesar introduced a new calendar to replace the old Roman one, which was too inaccurate. His new Julian calendar had 365 days divided into 12 months and an extra day every 4 years. It was slightly changed by Pope Gregory XIII in 1582 and called the Gregorian calendar, but remains the basis for the calendar we use today.