I'll have to go along with the Decline and Fall of the Roman Empire as well.
There are some similarities and correlations:
Frontier
Rome started to stagnate when there were no more frontiers they were pushing into. Essentially, they stopped at the limits at which figs, olives, and grapes could be cultivated. Without new frontiers and conquests, Rome started to stagnate toward eventual collapse.
America's growth and current size is also related to frontiers. The westward expansion across the continent. The frontiers of science and technology during the Space Race and rise of computer technology and the internet. But, America is no longer the leader in many technologies and sciences. Other countries are taking the lead. America's ever declining education system is a large factor in this decline. America really has no true frontier now and is becoming stagnant.
Armed Forces
Look at who fought for Rome during it's history in it's legions. Able-bodied, property-owning male citizens during the early years, then supplemented by auxiliaries, who were not Roman citizens, then became a professional force drawing from the poorest classes to fill it's ranks, to eventually hiring mercenaries to fight for Rome as it's own citizens were less apt to fight for Rome themselves.
America's armed forces followed a slightly different path. Professional soldiering was well respected, more or less, up until the 60's. There have been periods of conscriptions. In the past few decades, America has gotten other countries to fight by Proxy and has even gone back to the use of mercenaries in the form of Contractors and Private Military Companies (Mercs have been a constant throughout history for the most part, save the decade between the 70's and 90's due to tales from Africa, professional standing armies are more rare than mercs in history).
Americans are less likely to volunteer to serve (military has trouble meeting the larger end strength numbers approved by Congress without huge bonuses, and today's military is small, percentage wise, to many times in our history), less likely to serve a long term, and as a society and politically against putting it's troops into combat for extended periods.
Barbarian Uprisings
Rome had uprisings along it's borders, sensing the decline in Roman might, and striking where they could. Their military was overstretch to meet the threats and thus Rome was sacked.
America has terrorists sensing the decline in American resolve and hitting where they see weakness. The military is overstretched trying to meet the threat.
Dependent on Foreign Resources
With Rome, it was primarily wheat and grain from Egypt that kept the mob at bay and fed.
With America, it is cheap foreign oil that we are dependent on. Also, most of America is "owned" by foreign interests in the world economy.
Second Class Citizens
Rome had it's slaves. Toiling away to support the empire at every level. Slave riots were not unheard of.
America has illegal immigrants now, toiling away to support the agricultural and construction industries of the nation. Slaves, slave riots, and race riots also in America's past.
Bread and Circus
Some similarities can be found between the major entertainments for the masses for each time. For Romans it was gladiators, public executions, chariot races, animals vs humans and the like. Blood, violence and gore were popular. Drug /drinking use was a problem for both times. As long as the mob had food and entertainment, they were controllable.
In America, you've got "pro wrestling" with 5 year old kids in the stands yelling "kill him!", football actually becoming more violent off the field, NASCAR, hockey, video of when animals attack and criminals being taken down by law enforcement, horror movies,... even in the news, "if it bleeds: it leads" is still the norm. As long as the proles have t.v., entertainment, and fast food, they are controllable.
Self Important Arrogance and ignoring Crumbling Infrastructure
Rome was certainly arrogant in it's own importance and looked down on all "barbarians". Near the end, public works started to fall into disuse and disrepair. Many cities in the Roman Empire were not safe to travel at night.
America holds some self important arrogance as a nation of peoples. Beyond national pride there are many that truly feel America is the best country on the planet without question, but the facts are it's place among the world community in matters of health care, education, life expectancy, child mortality, economics, standards of living, and other areas has been slipping for years. America is still a great place to live in general, and some places in particular, but it does not really hold the top spot in any category you care to mention beyond the strength of it's military might.
Add to that America's infrastructure is crumbling. Bridges, roads, canals, levies, the power grid, reservoirs and dams, water systems. It's all in need to repair and upgrading, yet politicians and special interests funnel money to "new" projects. That rot extends to inner cities and despair in some communities and overriding crime.
Politics and Politicians
Early Rome and Early America's politics and politicians were both generally of better character, lower frequency of graft and corruption, and actually served the people much better than the quality of politician they would get latter in their histories.
Late Roman government was little more than elected positions bought and paid for with cash. Halls of government filled with corruption, abuse, and self interests, and Rome and the people suffered in the end.
America's current government and bureaucracy.......
Religion
Rome saw the rise of Christianity. America sees a bit of resurgence in religion these days.
