BB&T Bank — they will flat ruin you!
I have had access to my direct-deposited funds on the same day, but the online banking is a big problem. It is true that you cannot know your actual balance online, particularly if you use the debit card. It seems the balance only reflects a nominal portion or maybe a percentage of the actual amount debited and it won't post the full amount or where it went to until 2-3 days later. So those funds look online like they're available to you, but you'll get burned with fees later when you find out that the balance is entirely inaccurate.
I deposited a payroll check from a second job, as well as a state tax refund check on Wednesday morning and it wasn't credited until Thursday. And here's the fun part, which I'm battling with them on at the moment:
At my full-time job I have direct deposit, am always paid on Fridays, and I use their online bill pay set up to have all my bills come out on payday Fridays. I discovered this morning that they changed my payment date on all my currently due bills to THURSDAY. I didn't tell them to do that. They didn't send me an email to let me know anything about why I might need to check my payment dates and make changes. They just changed it. So, of course now I am hit with nasty overdraft fees because they paid my bills out of my account on Thursday but of course my payday didn't change, I still got paid on Friday.
This is theft, and I told them so.
I am done with BB&T. They will flat ruin you. They don't credit your deposits until after they pull your debits, so this is another way they get rich off of responsible, hardworking people who think that once they make their deposit that they should have access to their money (in this day and age, when they can make automatic deductions the second you write a check, there is no excuse for there not to be). It's just wrong.