"A Chronicle of the Last Pagans" by Pierre Chuvin looks at the sharp decline of Greco-Roman pagan religions and philosophy in the 4th century AD. The last pagan Roman Emperor of Rome was Julian. His reign was short, 361 to 363 AD, and was noted for a short lived attempt to return the old gods to prominence. Yet this was not a popular policy and even before Julian died, a large temple to Zeus was torn down in Antioch, Syria. When the temple of Zeus was destroyed, a small element of Zeus devotes thought Zeus would strike down the Christians with his thunderbolts. When the dust cleared and nobody was struck down by lightning, it pretty much ended the cult of Zeus in Antioch, which was one of the larger cities in the Roman Empire.

My comments here talked about this, with the comments on paganism in the Later Roman Empire and the Byzantine Empire being perhaps the most useful. The decline of paganism was gradual and despite the work of a lot of historians, we just don't know exactly when paganism lost its influence - I'm inclined to believe that it is impossible to decide when ideas truly died out, since they were often partially adapted for other circumstances.

Some historians argue for an early death, such as Alan Cameron, whilst others like Neil McLynn (and me personally) see paganism as an influential force even in the fifth century. There is also plenty of evidence for paganism amongst the privileged elite in the Byzantine world until at least the late-sixth century - they were secretive and persecuted, but it still clearly had an influence! Moreover, pagan mythology and philosophies were adapted for Christian use, especially in art and literature, so elements of Greco-Roman religion never entirely disappeared.

I hope this vague answer is useful - let me know if you have any questions :)