How did Rome's contact with the Hellenistic world affect Roman civilization in the second and first centuries B.C.E.?

This is a very complicated issue, but in some ways we can
say that the Roman aristocracy had a kind of love-hate relationship with the Greeks.  On
the one hand, many elites were fascinated by Greek art, literature and philosophy. 
Having a Greek slave to tutor one's children was a sign of great status.  Even Cato the
Elder, who feared Greek influence as corrupting the old-fashioned Roman mores, saw the
value of having a Greek tutor for his son. Greek cultural influences led the Romans to
write their own history (Rome's first work of history by the senator Fabius Pictor was
actually written in Greek, in order to explain the Romans to a Greek audience),
literature and poetry in conscious imitation of Greek models, but eventually these
attempts became distinctly "Roman" in character.  A nice example of this would be
Aeneas, a hero from the Greek Trojan War myth, who became the founder of the Italian
people in Vergil's epic the Aeneid. His quality of
pietas (devotion to duty) was a trait the
Romans imagined themselves to possess in abundance.  The extensive trade networks of the
Hellenistic states brought goods from India, Persia and as far as China into Roman
markets.  We hear of Chinese silk for sale at Rome in 55 B.C.E.  The Roman poet Horace,
who based his own Latin poetry on earlier Greek models, perhaps said it best when he
said, "Captured Greece captured the Roman conquerors." 

On
the other hand, wealth derived from the conquest of Greek lands, especially the
fabulously rich kingdoms of Pergamum, Pontus and finally Egypt, upset the delicate
balance of Rome's political system.  Massive numbers of captive slaves from conquered
kingdoms and cities in the Hellenistic world undermined independent Italian peasant
farmers, who could not compete with the huge slave-worked estates of the Roman
aristocracy.  These farmers often left their land for Rome, where they contributed to a
rapidly growing and overcrowded city.  Meanwhile, the highly competetive Roman elite
could use these dispossessed people as clients, bodyguards and, ultimately, soldiers in
their own armies.  The clearest illustration of the relationship between the desire for
wealth generated from conquest, and the increasingly chaotic political system, is in the
actions of L. Cornelius Sulla.  Sulla, deprived of a lucrative military command to put
down the Hellenistic monarch Mithridates, fought his way into Rome in order to retrieve
his command.  Later, in the first of several civil wars in the first century B.C.E., he
fought his way in a second time in order to punish his political enemies who had
deprived him of the command in the first place.  The intense competition among Rome's
elite, and the senators' willingness to use wealth derived from the conquest of the
Hellenistic world, for their own political ends, contributed to the ultimate collapse of
the Republic.