The problem there is that all it takes is one crap site and an attacker can check all of your "reset answers" (pet's name / mom's name / etc) to see if they can be used for an attack.
These bullshit "security questions" are actually the weakest link. I don't use them. If the site enforces it, I fill them with noise.
Think about what the minimum information an attacker would need to access your bank account (either login or social engineering) and then look at how many sites have that information.
Depends on your bank. Mine doesn't let me log in with username or password or any such crap. Also, every bank worth its money these days will use 2-factor authentication, or send a TAN by SMS or something like that. More and more banks will also send you SMS to inform you about every transaction made, so you can stop any abuse immediately.
Banks are among the few who actually take security seriously. They're not perfect, not by far, but they are still among the only commercial entities to use one-time-passwords (those TAN lists) and were among the very first to use 2-factor authentication.
So, to answer your question: What do you need to access my bank account? Nothing you would find on any of the forums, games sites or even my Amazon or iTunes account.