It's common to pay a reading fee when entering contests. Funds often go toward the running of the contest, including an honorarium for guest judges. However, it's good to be careful when asked to dole out money. There are plenty of unscrupulous tricksters out there happy to help you part with your money knowing you'll be smitten by the possibility of a prize, publication, or feedback.
Only submit to contests run by reputable organizations with which you are familiar. Many well-established journals run annual contests, as do writers' organizations. Also, be sure the reading fee is in proportion to the award. It's not uncommon for a contest with a $1000 prize to have a $10-$15 reading fee. That's a general range. Some legitimate contests run higher. And some have no reading fee at all. If the fee is $50 and the winning prize is $100, you might be getting ripped off. Be careful, as sometimes fees are attached to other aspects of a contest. For example, there's the contest where any entry is published in the special anthology—for a hefty fee. Or the editing service that runs a contest to find new customers. One or two "winners" get a prize, while the rest of the entrants get the hard sell to purchase their services.
A brouhaha erupted over contest practices in 2004 when Zoo Press cancelled its prize without awarding a winner and kept all the entrants' submission fees. This sparked a big debate in the industry. Since then, the Council of Literary Magazines and Presses released a code of ethics for running contests. Some contests adhere to this code and say as much on their website. Overall, it's made organizations and writers more aware of ethical concerns in contests.
If you're submitting to reputable contests backed by organizations you respect, you shouldn't have a problem. And always remember to read guidelines in full. If you're not comfortable with any of the stipulations, don't submit.