I used to have Bank One when I was about 12 or so but then they got bought out by Chase. (actually the bank was something else before Bank One). I still have Chase. I've had a few issues before with Chase but I'm still with them.
There was one time when I had a joint account with my dad when I was a teen and around 8pm the security dept from Chase called my dad asking about whether or not we wired $1k to Mexico. They asked about a debit card that I just got rid of. It was when you had to go in the branch and they took your card, destroyed it, and you had to wait a week to get a new one in the mail. I remember giving the employee my debit card and he was supposed to destroy it. My guess is he used it to wire money to Mexico. In the end, they gave me back my money right away while they did an investigation so I wasn't out anything.
One issue I did have was when I was paycheck to paycheck many many years ago and I knew I was going to overdraft when I paid some bills, I planned out my transactions to minimize the amount of overdrafts I'd be charged by the way they did their transactions at the end of the business day. Low and behold, they silently changed their policy on how they charged overdraft fees/transactions and I got hit hard. I chatted with them to see if they can reverse some of the overdraft fees. Even if a few fees. They denied it so I complained and filed a complaint with the Attorney General's office for their shifty practices (in my eyes). The AG forward a copy of the complaint to Chase and I got reimbursed half the fees.
Other than that, I haven't had many big issues. I like Chase.