Depends entirely on the card! Annual fees can be either $0, as small as $30/year, or as high as $500/year (AMEX Platinum) and up. AMEX Centurion is invite only, it's for millionaire high spenders and has a $2,500/annual fee. Barclays Luxury Card is open to everyone and I believe it has a $900/year annual fee.
Some cards waive the annual fee the first year and some don't. It's whatever the card issuer decides makes them the most money.
Personally, I pay two annual fees and have a third one waived for now. Some of the cards I have I've downgraded to the less benefits no annual fee version of the card after collecting the annual fee version benefits for a year.
Many, many cards have no annual fee. The ones that do, are usually worth it for the right customers- e.g. a travel card that comes with a lot of actually-valuable travel perks for the frequent flyer.
Credit cards with an annual fee simply for the privilege of having a credit card, are mostly gone, chased out of the market much like the takeover of free checking.
Wow. I'm taking it you don't have to pay an annual fee for having a credit card in the US.