Yes, some of the nation's largest banks should be broken up in order to prevent another financial crisis. The serious financial crisis that the country has faced in recent years way promoted by large banks that most though could not fail going under. In order to avoid this situation again steps should be taken to break up some of the banks.
The obscene profits generated by the nation's largest banks, and the salaries paid to their executives, is enough to alter the entire economic landscape of the United States if redistributed and fed back into the country. The banks have enjoyed political favors, lax regulation and indifferent media coverage to conduct business as usual in a variety of guises - time to try something new.
The nation's biggest banks should not be broken up to prevent another financial system crisis because the problem is not with the size of the banks, but rather the government involvement that created the financial mess in the first place by encouraging lending to consumers who were in no position to take on certain financial obligations.
Introduce risk proportional to their size, or rather, their ability to impact the national or international economy. Let them grow, but put some real consequences in place. The "with great power comes great responsibility" holds true. Make them keep enough cash in reserve to survive a crash. Make laws that will hold management more responsible. Put some real punishments in place in the form of fines and jail time proportional to the size of the failure.