I am already reading Edward Gibbon's The History of the Decline and Fall of the Roman Empire, and while research since its conception may have disputed certain facts unknown at Gibbon's time (it was published in 1776), it is still an excellent detailed account of the Roman Empire from 170s and onward, without ever getting boring, because of Gibbon's excellent prose.
Check out "The History of Rome" podcast by Mike Duncan, for a highly enjoyable and thoroughly researched account of Rome from ~400BC to the last Western emperor.
A good popular history of the other side of the "Fall of the Roman Empire" is "Terry Jones' Barbarians".
I scare-quote "Fall of the Roman Empire" because even though Rome itself was sacked, the Eastern half of the Roman Empire kept going for another millennium, though known to us moderns as the Byzantine Empire (it was known to all contemporaries merely as The Roman Empire).
