Redneck Bank Mega Money Market Account is up to 1.5% APY up to $35,000. It's the best FDIC insured account that I can find that doesn't have monthly usage requirements and isn't an introductory rate only. One of the things I REALLY liked with Redneck is when I called their customer service line, I got a human being on the phone immediately--no automated attendant, no press "1" for this, press "2" for that. And the person knew the business, and was helpful immediately--no accent that made it difficult to understand, no trying to find the answer to my question on a list, no putting me on hold, no transfer to a level 2 help desk, etc.
I use Barclays Bank Dream Account (1.15% APY) for my kids. It's got some nice features such as additional interest rate bonuses if you don't withdraw for 6 months. It's also kid friendly and can be set up with an adult account to access childrens' accounts.
For checking, the best that I've seen is Lake Michigan Credit Union (LMCU) which offers 3% APY up to $14,999. But I believe there are some usage restrictions.