There are several triumphal arches in Rome, but the most famous of them all is the Arch of Constantine. This arch is located between Colosseum and the Palatine Hill and was raised in memory of the big victory of Constantine facing Maxentius in 312.
Another triumphal arch in Rome is the Arch of Titus. This one is also in the area between Colosseum and Forum Romanum and was built in honor of Titus defeating the Jews in Jerusalem around 70 AD. This was used as a model as they created the triumphal arch in Paris much later.
If you have time to read historical books and later look at the arches it is very interesting to see what the different signs, pictures and writings on the arches symbolize. Sometimes they speak of a certain part of the battle and like on the Arch of Titus you can see how he marches celebrating the defeat of the Jews with articles from the Temple of Jerusalem in his hand.