They certainly had a mentality of ''might is right'' that led to brutally cruel things. I forget the exact quote, but Caesar wrote something along the lines of ''the victor is allowed to do whatever he likes to the defeated'', which gives you an idea as to how they generally thought.

Mass infanticide is not something I ever came across whilst studying my masters degree in ancient history - although you could potentially argue that they allowed their client king Herod to do something along these lines, depending on the accuracy of the events depicted in the New Testament. Genocide is perhaps a more difficult topic, as the Romans certainly eradicated cultures and civilisations in their conquest of the Mediterranean, Carthage perhaps being the most infamous example of this. However, enslavement was far more profitable than simple execution, which leads me on to the war rape you mention. Prior to Augustus' reforms in the late 1stC BCE, Roman soldiers received the majority of their pay from looting cities and being awarded farmland on retirement - this led to loyalty to popular generals who gave them these over the state. Therefore, on taking cities the raping and pillaging was usually widespread. I remember a site in Spain destroyed in a Roman siege (I forget which one, maybe Numantia) where a skeleton was excavated that had several spears inserted up every orifice going. Sieges were awful, but hardly typical events of life in the Roman Empire. The reliefs on Trajan's Column also depict plenty of awful scenes found in being defeated by Rome.

That being said, daily life in the Mediterranean was, by and large, at its most peaceful and prosperous until the modern era once the Empire was settled and stablised in the first and second centuries. The brutality that we hear about was usually extremely rare and acted as a deterrant. Basically, if you rebelled against Rome, they'd put you down with a hell of a lot of force to make an example of you (see the Jewish Revolt or Mithridates VI of Pontus, for examples), but by and large they certainly did not rule with an iron fist. Punishments such as crucifixion were definitely cruel, as were public executions in the arena, yet considering the Romans introduced organised law and prosecutions in many regions they can therefore perhaps be considered as advanced for the time.

For anyone interested, Luttwak's The Grand Strategy of the Roman Empire is a thought-provoking (and controversial) look at how Rome operated, written by a non-expert. If I remember correctly Luttwak was an American diplomat during the Cold War.

I've never heard anything about genocide by Romans, do you have a source for that because it sounds interesting.

The Romans were the only ones who were not "barbaric", in the literal sense. Barbarian was a term they used to describe non-Romans. It's interesting that now they would be considered barbaric today.