What tips and tricks do people use to keep the cost of banking down?
You really should be able to avoid bank charges entirely. If you're paying for a checking account, know that there are ones available for free, even without a minimum balance. Same goes for credit cards. There are plenty of no-annual-fee cards out there, so unless you're getting fabulous rewards that make it worth it, never pay an annual fee. Avoid ATM fees by avoiding the ATM, getting cash back at stores or taking it out at the bank. Overdraft fees and other penalties can be avoided by keeping an eye on your balances and keeping a register.
Take advantage of email or text notifications that many banks offer when your account balance goes below a certain amount, or your credit card gets close to its maximum.
And I agree with MrChrister that many fees will be refunded if you've made a one-time mistake. Talk with a customer service rep, apologize, emphasize that you have a good record of on-time payments, and ask if the fee can be taken off your account.
One thing I do is make a point of maintaining a minimum monthly balance in my chequing account, sufficient to avoid the regular monthly fees. Many banks have accounts that work like that, i.e. where they'll charge the monthly fee only if your balance dips below a set level in the month. I've been dinged a couple of times though when I wasn't being careful. Even temporarily dropping below the threshold (e.g. on one single day) is enough to trigger the fee - it's not an "average daily balance" thing. Now I will move money in from elsewhere if I'm getting too close.
I also make a point of only using credit cards that have no annual fee. I used to have a ton of reward cards with special features and annual fees to match, but I realized I wasn't getting enough rewards to justify the costs when I added them all up.
Simple: Don't use banks.
Banks are for-profit entities that are, by design, always trying to find new ways to increase their profits, and those profits come from customers, aka YOU.
Do some research and you will likely find a Credit Union that you are eligible to join. Credit Unions are owned by their customers (usually called "Members") and work more like a non-profit. When the Credit Union does well, it tends to use the profits to increase interest rates, decrease loan rates, or pass along the benefits to the customers in some other way.
Check out NCUA.GOV for more information.
Budget and plan ahead. Always pay your bills on time and plan so you don't over draft.
If something goes wrong, a sweet tone of voice and an office visit has earned me sympathy and reduced overdraft charges in the past. The bankers at my bank (US Bank) have the power to just waive fees if they like.