This is the government-sponsored site that is the only true place to check credit. You get a free credit report from each of the 3 credit bureaus once a year. You won't have to enter any credit card info into this one to access your reports.
This site provides a decent overview of what goes into your credit score, but beware that there are different types of scores a lender can pull, so this may not reflect the credit score a lender sees when running your credit.
For now, the FICO is the most popular score. We suggest our clients focus on the credit report and improving the underlying information there as opposed to paying for the score, but curiosity gets the better of people sometimes!