What are your favorite Rome-screw scenarios? Basically, the ones in which Rome's supposed favour amongst the gods fails them at crucial moments in military and political history? Covering the period between the founding of Rome (753 BCE) and the fall of the city to Odoacer (476 AD).
I'll throw out the Second Punic War, Roman-Seleucid War, Cimbrian War, Mithridatic Wars and Roman-Parthian Wars as my favorites from the Republican and early Imperial Eras.
Carthage could have created a mercantile empire in the Western Med.
The Seleucids could have pushed all the way to the Aegean, and estabilished a friendly puppet pharaoh over Egypt.
The Cimbri and Teutones could have settled on the Pannonian plain, creating the situation of a dagger on the throat of Italy.
Mithridates VI of Pontus could have expanded his kingdom to varying lengths. IMO, if victory for him comes during Sulla's time, he'll be able to expand Pontus all the way to Achaea. OTOH, if victory comes during Lucullus' time, then he'll find difficulty in expanding beyond Asia Minor, and will still find himself dependant on the Armenians.
The Parthians and early Sassanians could also have expanded into Syria on numerous occasions.