Banks don't make this easy. There isn't a secure way of doing it in the vast majority of cases. Companies like Digit use Plaid to offload the risk of storing these credentials (like how most startups offload PCI/credit-card to Stripe). Intuit's big enough to have their own solution for Mint.
So, they're just punting the liability to another 3rd party (Plaid)? Given all the excitement in this thread, I was hoping that Plaid had miraculously cajoled the banks into an OAuth integration.