My AMEX points work out to 1.33% and my Capital One gives 1.5% . Both are statement credits. I haven't personally seen or been offered anything better than Capital One for that type of incentive.
I'd guess some points/loyalty hacker has figured out how to get over 1.75%, but it probably wouldn't be cashback through direct statement credits.
I'm in Canada, not the US, but I have one that gives 4% cash back on gas and groceries and 2% at pharmacies and for bill payments.
There is a Fidelity-branded Amex card that gives 2% on everything, with no annual fee. There are several other cards that give 2% on everything (Capital One Venture, Barclay Arrival+) but that bear annual fees.
I used to have an HSBC card that offered 2% cash back on weekend purchases. Capital One acquired HSBC's accounts a few years ago and no longer offers that deal.
Fidelity Amex offers 2% on everything with no limit.
My AMEX card has 1%/2%/3% depending on merchant category. The higher %s are also capped at some level.
I know discover is planning 5% amazon rewards in q4.