which credit card gives the best rewards(cash back or gas cards) with no annual fee?

I'm not sure which country you're in but try moneysavingexpert.com or moneysupermarket.com - both sites giving advise on UK financial products.

in canada TD and CIBC are good choices for reward cards

Here are three of mine, no annual fees on any of them. Last year I figure I earned about $1000 bucks from my credit card companies. I charge everything I can even if I have cash, because reward dollars are free money. Obviously, you need to spend within reason – if I cannot pay it when the bill comes in 30 days, I will not buy it – but if I am making a purchase, this is what I use.Discover - 1% back on all purchases. Additionally, they run 'specials' on their web site that you can sign-up for. This month it is 5% back on gas and automotive repair. Amex Blue - 1% back on all purchases, 1.5% back on 'Everyday' items like drug store items. Like Discover, a few times a year they run specials with bigger rebates on home improvement stores or gas fill-ups, etc.Chase Disney Visa - If you have kids, this could be the card for you. 1% back on all purchases that can be turned into "Disney Reward Dollars" and redeemed at Disney World, the Disney Store, Disneyland, etc for cash. Talk about a bargain…nothing like take the kids to see Mickey on Chase Visa’s dime.