Back in January, Consumer Reports Travel Letter said

"Those who generate less than $7,500 in charges annually are 'not spending money wisely,' says consultant Randy Petersen, president and CEO of Frequent Flyer Services. Your alternative is to get a no-fee bank card with a low annual percentage rate (APR) and buy your travel."

$7,500 not be a firm threshhold. For example the Starwood Amex card awards 1 mile per $1 for a $30 annual fee.

But do compare discount fares to where you normally travel vs. annual fees for the number of years it takes to get an award. Don't forget paid travel usually awards bonus miles while reward tickets do not.