It wouldn't have prevented every part of the subprime crisis (Bear Stearns wasn't even a deposit bank), but it would potentially have lessened the scope of the crisis.
- Preventatively, it would have restricted the size of the CDO/CDS market. Without access to commercial banking deposits there would have been much less money to invest there.
- Reactively, it would have better protected deposits and saved the FDIC a small fortune. Indymac alone ran the FDIC $9 billion and depositors another $0.27 billion.
Its decline and repeal completely reshaped US investment banking, to the point where the entire industry would have looked completely different if the law had been applied 1933-2008. Of course, that's not entirely a good thing.
Some chunk of the pre-2008 growth has to be attributed to a flexible banking industry keeping us out of liquidity traps, and that was a genuine, non-special-interests reason to alter the law. Clinton didn't (exactly) repeal Glass-Steagall, he formalized a change that regulators had made far earlier by limiting enforcement of the firewall.
I can't say that long-term enforcement of Glass-Steagall would have been better, but I can certainly say that it would have altered the entire landscape that the subprime crisis happened in.
The basic theory of Glass-Steagall is to separate risk-taking in finance with the "mundane," finance, as Krugman was saying.
On one side of the coin in finance, you have the boring finance: home loans, small business loans, that day-to-day stuff is not complicated and is necessary service to the economy. By the way, we can't let these banks "fail," or go out of business. That would cause economic destruction beyond what is reasonable. Fortunately, this type of banking is not very risky, either.
Now, you have the other side of banking, which involves risk-taking. Some of this is stuff such as investment banking and private equity which is actually very necessary for efficient allocation of resources. These types of businesses need to be allowed to fail, though, since not letting them fail would be a redistribution of wealth from the taxpayer to the rich, and it would also mean people who are not good at efficiently allocating resources get to keep their jobs while smart people who can do it better, get crowded out by the politics of government handouts.
Also on the risk-taking side of finance you have securitization and a lot of "financial alchemy," stuff. Fannie Mae and Freddie Mac arguably even fall in this category. This side of finance needs to also be allowed to fail for the same reasons.
I hope that makes sense. I recommend picking up an intro and intermediate-level macroecon textbooks for further reading.