I have...
USAA for my insurance needs only.
Bank of America for unlimited bill pay. BoA will cut a check to ANYONE I want them to. Just takes 2 seconds to set up a payee. When you pay the bill, the money is taken out of your account within 2 business days. No monthly fees if you have direct deposit and only a checking account. I do think they charge a fee if you have a Savings account under their minimum balance. So, I don't have a savings account with them. You do have to pay for checks. And if you don't use a BoA ATM, BoA charges you $2, and the ATM will charge you whatever.
I used to use Navy Federal Credit Union for my TAD travel claim deposits only. To keep them seperate from my main account so my wife doesn't see the money and think "OOOH SPENDING TIME!". Now, I just have my rent going into there so I can cut a check from that account. Once a year they have a great interest rate for transferred balances. I think like 5.9%. The rate is good until the transferred balance is paid in full. I didn't use theirs though. Navy Federal is a good bank, though. Service centers and ATMs just about everywhere the Navy is.
Langley Federal Credit Union in Virginia is decent too. I DID get a credit card through them and transferred some higher interest rate balances to their 5.9% card.
Honolulu Federal Employees Federal Credit Union (shew!) was GREAT when I lived in Hawaii. They ALWAYS had the lowest intrest rates.. and actually, still have very low rates. Down side is, if you want to finance a car, you have to live in Hawaii. However, I did get a good bill consolidation loan from them while living in the lower 48.
Think I'm also a member of Sea West Federal Credit union in the San Francisco Bay area. They always had helped me out when in a pinch. I remember I called up once, told them I might have to pay for repairs on a car I had financed through them. She said, "Hold on". And litterally was back on the phone within 30 seconds and asked how much. I told her $500 she said no problem, check is in the mail today. I don't think they're that liberal anymore.
I leave my credit union accounts open if they have a balance just to keep their free $1000 accidental life insurance open.

May only be $5 in the account, but hey, why not.
Only reason I stick with BoA is for the completely free online banking. I hate writing checks, licking envelopes and buying stamps.
Key is to do just that.. shop around.