Citibank is the poster child for this problem, though the bank has a very long history of being on the wrong side of collapses (they were deep in Mexico and Asia when both needed bailouts).
First, let's look at the Glass-Steagall act of 1933. It was a New Deal law, which was enacted in response to abuses preceding the Great Depression, where bankers were pushing depositors to invest in dubious stocks that they were also being paid by the company to sell.
Basically, it made it illegal for a commercial bank to operate as an investment bank, and vise verse, because there are too many conflicts of interest created when commercial banks are permitted to underwrite stocks or bonds".
Bill Clinton delivered his "New Democrat" party, accompanied by lots of happy talk about magic words like "synergy" and how "modernization" would create a more stable (and profitable) financial system. It did the latter, for sure, but not the former.The problem is, of course, that Citi is so large that the consequences of its failure would be disastrous to the markets. It would make the collapse of LTCM, which reaqired a Fed orchestrated (Alan "Bubbles" Greenspan) bailout look like the failure of the corner 7-11.
Actually, the combination of insurance, investment banking and old-line commercial banks multiplied the conflicts of interest within banks, despite so-called "firewalls" supposed to keep these activities separate. Much like Enron, placing some deals in off-balance sheet entities did not insulate Citigroup from the losses in its swollen subprime housing lending. The bank has so far written off something like $15 billion and more to come.
Over the past few years it has appeared that the every single rollback of Depression Era regulations has been a mistake.