An Arch is a curved structure spanning an opening, formed of wedge-shaped parts resting at the two extremities. A triumphal arch is a structure in the shape of a monumental archway.
Commemorative arches are large monuments built to honor important men or events. The Romans erected commemorative arches, called triumphal arches, to emperors and generals, celebrating military victories.
Here's a collection of Roman triumphal arches built in the different parts of the ones mighty Roman Empire.
The Arch of Titus - Rome, Italy

To commemorate the sack and capture of Jerusalem in 70, which effectively terminated the Jewish war that begun in 66, Emperor Domitian constructed a Pentelic marble triumphal arch with a single arched opening, located on the Via Sacra just to the south-east of the Forum in Rome and was called the Arch of Titus. It was built shortly after the death of Domitian's older brother Titus (born AD 41, emperor 79-81). The Arch of Titus has provided the general model for many of the triumphal arches erected since the 16th century.
Trajan's Arches
Many triumphal arches were built in honor of Emperor Trajan. The Arches of Trajan were built in the manner of triumphal arches (although they do not celebrate military victories) in a number of places in the Roman Empire during the reign of Trajan. By contrast, when it came to commemorating his military achievements in Rome itself, he chose a column rather than the more standard arch. The Arches of Trajan include
The Arch of Trajan in Ancona, Italy

The arch is built of marble and stands 18.5 m high. It was erected in 114/115 as an entrance to the causeway atop the harbor wall in honor of Trajan's creation of the harbor there. Most of its original bronze enrichments have disappeared. It stands on a high podium approached by a wide flight of steps. The archway, only 3 m wide, is flanked by pairs of fluted Corinthian columns on pedestals. An attic bears inscriptions. The format is that of the Arch of Titus in Rome, but made taller, so that the bronze figures surmounting it, of Trajan, his wife Plotina and sister Marciana, would be a landmark for ships approaching Rome's greatest Adriatic port.
The Arch of Trajan in Benevento, Italy

The people of Rome and the senate erected an arch to honor Trajan in 114. It has important relief relating to his civil and military deeds and virtues and the history of the Via Traiana (whose entrance into Beneventum it marked). It was enclosed in the walls on its construction but it is now free-standing at the end of a vista.
The Arch of Trajan in Timgad, Algeria

This triumphal arch rises at the west end of the decumanus called Trajan's Arch. It is 12 meters high and was partially restored in 1900. The arch is principally of sandstone, and is of Corinthian order with three arches, the central one being 11 ft wide. The arch is also known as the Timgad Arch.
The Arch of Trajan in Merida, Spain

This arch was erected in honor Trajan, the emperor from 98-117, he was born in Hispania. The arch marked the entrance of the provincial forum.
Arch of Constantine - Rome, Italy

To commemorate Constantine's victory over Maxentius at the battle of Milvian Bridge on October 28, 312, the Arch of Constantine, a triumphal arch was erected in Rome. It is situated between the Coloseum and the Palatine Hill. Dedicated in 315, it is the latest of the existing triumphal arches in Rome, from which it differs by spolia, the extensive re-use of parts of earlier buildings.
Arch of Janus - Rome, Italy

The only quadrifrons triumphal arch preserved in Rome, across a crossroads in the Velabrum-Forum Boarium is the Arch of Janus. It was built in the early 4th century of spolia, possibly in honor of Constantine I or Constantius II. Its current name is probably from the Renaissance or later and is not ancient. The name is derived from its four-fronted, four-arched structure.
In the Middle Ages, the Frangipane family transformed the building into a fortress and so it survived intact up until 1830. Then the attic and top were torn down because they were erroneously believed not to belong to the original structure. Fragments of the dedicatory inscription are still preserved inside the nearby church of San Giorgio al Velabro.
Arch of Augustus - Rimini, Italy

This arch was built in honor of Caesar Octavianus Augustus. The Arch of Augustus is situated at the meeting point of Via Flaminia and Via Emilia in the city of Rimini in Italy. The engravings on the monument states that the history of the monument dates back to 27 BC and it is the oldest surviving Roman arches in the world. The Arch of Augustus, Rimini is a popular tourist attraction in Rimini.