Internal instability leading to strife and corruption, partially caused by several subsequent invasions.

cause they were stupid

It was getting too big and spread out to manage. I don't know any accurate details, but it includes political conflict within Rome itself, topped by Neron who was just completely insane and was playing his violin while Rome was burning. :/ At least, he's an iconic figure as far as the downfall of Rome went, even though as a ruler, he was apparently very successful for a while. Towards its end, Rome was sacked and attacked by surrounding barbarian tribes, which didn't help matters none.

There are many reasons. There was an influx of other peoples into Roman territory (Huns, Goths, Vandals etc) which put economic strains on the empire. It was also huge, managing such a large area was nigh on impossible (the Empire wasn't even a single entity at the time of Rome's fall but divided into Eastern and Western - the Eastern persisted for a long time after the collapse on the western). There were weak emperors notably Honorius who was emperor when the Goths under Alaric sacked Rome. Centralisation also played a part. I could go on for a long while here (and many have) and there is still much debate. Personal thoughts are that it was over-extended, economically unsound and suffered from poor management of the influx of peoples from the East. The history of the Goths makes very interesting reading with regard to that point. Ultimately though no matter how large, powerful and self-described "eternal" something may be nothing lasts forever. AN interesting question that I think is sadly beyond the scope of this forum. There are many good books on the subject starting with Gibbon is not a bad idea (not saying I agree but it is a good place to start!) :)

The fall of Rome was due to various reasons. The republic fell before the empire itself but the reasons in which both fell are very similar. One, the government was corrupt. There was a lack of leadership and direction. During the fall of the empire there was 26 emperors in only 50 years. Human nature played a big role in planting the seeds of collapse. Also, long periods of peace ended up hurting the repiblic and the empire. People develpoed the attitude that nothing could go wrong and everything would take care of itself. General apathy rose and people stopped caring. Rome was unique and succsessful in its prime becuase people put Rome before themselves. Towards the fall, everybody was putting themselves first. The people of Rome lacked the morals that built the empire. Next, the economic situation did not help. The gap between the rich and the poor grew significantly. Rome failed to advance technologicly to keep up with their vast empire. Instead, various barbarian tribes began invading their lands.

It grew to big for its resources. Over time it became too greedy and less protective. As the army weakened, and the Asians (pushed west by the growing Chinese armies) crowded into Germany and lead to a great war. The badly fallen Roman army was unable to fight hard like they had 300 years before and the Asians and Gauls (of France) won the war conquering much of Germany and France. The armies of Asia and the North swept south and destroyed many Roman cities and villas. Finally in 476, they caputered and sacked Rome ending the 1,200 year long Roman nation.

Greed, corruption, and selfishness. Kinda like what's happening in the US.

There were many factors involved. Immorality, the use of lead in their drinking water, [and even their wines!] and the battle between paganism and Christianity all held a part of the answer. Basically, it withered from within, and collapsed under its own weight.

Long story short: The Empire was too big for Rome's armies to protect, and what sparse border armies it did have were too expensive to maintain. Basically, they had no choice to allow migrating tribes into their borders. Plus, with the growing military importance of cavalry, the mostly infantry armies of Rome were becoming out-classed by the 'barbarians' as well as out-numbered.