A few highlights (all bolding mine for emphasis):
During the Roman period a new legend developed concerning Dionysus, one that offers intriguing parallels to Christianity. According to this legend, Dionysus was killed while battling the enemies of Zeus. His body was dismembered, but Zeus restored him to immortal life. Henceforth, according to the late first-century Greek philosopher Plutarch, Dionysus became a dying and rising god, and a symbol of ever-lasting life.
Roman historians such as Suetonius and Tacitus frequently reported the occurrence of miraculous omens or portents regarding the emperors, particularly at the beginning or end of their reigns. Because Rome placed its rulers at the summit of human society, it was believed that they served as mediators for the will of the gods on earth.
According to stories recorded by the Greek historians Dio Cassius and Tacitus, Vespasian worked several healing miracles, while visiting the shrine of Sarapis in Egypt.
With his miraculous cures, Asclepius quickly earned great fame. Motivated by compassion, he even succeeded in restoring the dead to life.
Isis was worshipped continuously for thousands of years, before achieving her greatest renown in the early Roman empire. During this final period, her cult presented one of the most formidable and enduring rivalries to early Christianity
For debate:With the advent of the reign of Augustus in 27 BCE, life in the provincial cities of the Greek East became far more stable and prosperous than it had been for a very long time. The relief of the subject peoples was immense, and a number of the cities issued decrees honoring the new emperor as the earthly appearance of a benevolent god: "Providence. . .by producing Augustus [has sent] us and our descendants a Savior, who has put an end to war and established all things. . . ."
"The extraordinary claims made about Jesus were necessary to put Christianity on at least equal footing as any other religion of the time."
One final quote, from near the end of the article suggests why the 'cult of the emperors' would likely be viewed as a threat to Christianity:
Even more relevant to the rival message of the Christian gospels, however, was the gradual development of the relationship between the emperor and Zeus (Jupiter) himself, the sovereign ruler of the gods and the world.

