This post is basically an index of Roman ‘firsts’. Search this index if you are looking for the first time in history that the Romans staged gladiatorial fights, elected two plebeian consuls or used elephants on the battlefield. The links below will redirect to other posts where the events are discussed in more detail. Suggestions for more firsts are very welcome, as are corrections!
Third century BCE
292 BCE: first sundial in Rome (according to Plinius the Elder)
264-241 BCE: First Punic War
264 BCE: first Roman intervention outside Italy (on Sicily)
264 BCE: first gladiatorial games in Rome (as part of funerary games)
262 BCE: first recorded contravallatio, i.e. wall and moat facing outward (during the Siege of Agrigentum)
260 BCE: first use of the corvus boarding device on a warship
260 BCE: first naval triumph or triumphus navalis (for the consul Gaius Duilius)
256 BCE: first Roman campaign in Africa (under the consul Marcus Atilius Regulus)
249 BCE: first dictator to lead a Roman army outside Italy (Aulus Atilius Calatinus on Sicily)
242-241 BCE: first time two praetors are elected instead of one
241 BCE: Sicily becomes the first Roman province
238 BCE: first conflicts with the Ligurians
235 BCE: first ever closing of the gates of the Temple of Janus on the Forum Romanum
229-228 BCE: First Illyrian War
228 BCE: first participation of Roman athletes in the Isthmian games
227 BCE: first time four praetors are elected instead of two
223 BCE: first (and only) recorded use of the spears of the triarii by the hastati
218 BCE: first Roman campaign in Spain (under Gnaeus Scipio)
216 BCE: first of three Battles of Nola
215-205 BCE: First Macedonian War
215 BCE: the Lex Oppia becomes the first of many sumptuary laws in Rome
213 BCE: first (and presumably only) use of the sambuca naval siege ladder by the Romans (during the siege of Syracuse)
209 BCE: first plebeian curio maximus (Gaius Mamilius Atellus)
207 BCE: for the first time Roman coastal colonies are forced to provide troops for the Roman armies
207 BCE: first triumph of the Second Punic War (which started in 218 BCE!)
206 BCE: first Roman colony in Spain (Italica)
204 BCE: first celebration of the Megalensia, the games of Magna Mater
201 BCE: first grant of land to veterans from the army (probably)
Second century BCE
199 BCE: first use of elephants on the battlefield (by the consul Publius Sulpicius Galba in Greece)
198 BCE: first slave revolt in Roman history (probably)
197 BCE: first time six praetors are elected instead of four
196 BCE: first time epulones are nominated
189 BCE: first Roman actions on the island of Crete
189 BCE: first confrontations with the Galatians
188 BCE: the people’s tribune Gaius Valerius Tappo becomes the first to bypass the Senate in the legislative process
182 BCE: first diplomatic contacts between Rome and the Kingdom of Pontos
181 BCE: the Lex Baebia becomes the first law against electoral corruption (ambitus)
181 BCE: first gilded statue of a mortal man ever in Italy (of Manius Acilius Glabrio, in the temple of Pietas)
180 BCE: the Lex Villia Annalis becomes the first law to set minimum age requirements for holding the public offices of aedile, praetor and consul
180 BCE: first triumph for a victory without a fight (according to Livius; awarded to the proconsuls Publius Cornelius Cethegus and Marcus Baebius Tamphilus)
179 BCE: first stone bridge across the river Tiber in Rome (the Pons Aemilius)
172 BCE: first election of two plebeian consuls (Gaius Popilius Laenas and Publius Aelius Ligus)
171 BCE: first Latin colony in Spain (Carteia)
171 BCE: first use of the kestros against Roman troops (during the Third Macedonian War)
171 BCE: first known trial of a former provincial governor (Marcus Titinius Curvus; acquitted)
160 BCE: first treaty of friendship between Rome and the Jews (Maccabees) of Judea;
159 BCE: first water clock or clepsydra in Rome
157 BCE: Sextus Julius Caesar becomes the first of the Julii Caesares to hold the consulship
154 BCE: first Roman campaign against the Ligurians on the other side of the Alps (under Quintus Opimius)
153 BCE: (possibly) first Roman campaign in what is now Morocco (under Lucius Mummius)
153 BCE: first time the consular year starts on 1 January instead of 15 March
153 BCE: first time Cato the Censor ends a speech in the Senate with the opinion that, in his view, Carthage should be destroyed
149 BCE: the quaestio perpetua de repetundis becomes the first permanent court in Rome
139 BCE: introduction of the secret ballot for elections (Lex Gabinia)
137 BCE: introduction of the secret ballot for non-capital trials (Lex Cassia)
135 BCE-130 BCE: First Servile War on Sicily
131 BCE: introduction of the secret ballot for legislative assemblies (Lex Papiria)
131 BCE: first election of two plebeian censors (Quintus Caecilius Metellus Macedonicus and Quintus Pompeius)
111 BCE: first treaty between Rome and Leptis Magna in Libya
107 BCE: Gaius Marius becomes the first magistrate to openly recruit part of his soldiers from the class of the proletarii, the people without property
106 BCE: introduction of the secret ballot for capital trials (Lex Coelia)
106 BCE: first recorded use of the hollow square marching column (in quadrato agmine), with the baggage train in the centre, heavy infantry on all sides and cavalry, slingers and archers protecting the flanks (Marius in Numidia)
Third century CE
243: first time two brothers serve as praetorian prefects (Gaius Julius Priscus and Marcus Julius Philippus)
251: first time a Roman emperor is killed in battle against a foreign enemy (Decius)
259 or 260: first time a Roman emperor is captured by a foreign enemy (Valerianus)