Basically, I like the idea of managing my money and finances, but would love to build the software customized to how I manage my money. Quicken and Microsoft Money and the likes offer nice solutions, but not exactly what I want.
I'm curious how these applications are able to pull data from my financial institutions. I can't seem to find any APIs to get my data from Bank of America, Chase, etc.
How exactly do they do that?
It is not the bank that has the API but quicken. Intuit has published severial API's over the years that the the banks conform to. The standard is an open standard so other programs like Microsoft Money may use the same format for downloading data. Here are some links, Open Financial Exchange Format is the new standard everyone is using, Quicken Interchange Format is the old one.