Although you must be 18 in order to sign a legally binding contract, the age at which you can legally establish credit depends on a host of factors, including the type of credit you are seeking, state and federal regulations, and the individual policies of the credit issuer, as well as how you will be listed on the credit account.
For instance, if you're 16, you could obtain an auto loan, provided your parent, guardian or another adult (who is either 18 or 21 years of age or older, depending on applicable laws) agrees to serve as a co-signer on the car note.
Likewise, a teenager can acquire student credit card or a secured credit card, or you can be added as an authorized user to a parent's existing credit card. Any of these scenarios would help you begin to establish credit in your teens.
Generally speaking, most credit card companies require a credit card applicant under 21 years old to have a co-signer. And ever since the CARD Act was passed, federal rules have made it tougher for students to get cards on their own because you have to prove that you have the income to repay any debts charged.
Separately, someone entering college, say a 17- or 18-year-old, could certainly apply for and receive either federal student loans, which are backed by the U.S. government, or private college loans. Student loans also help to establish your credit rating.
For all practical purposes, however, you must generally fill out a FAFSA (the Free Application for Federal Student Aid) to be considered for a government educational loan. And that FAFSA requires data on the parent's income and debts. So realistically, your parents will likely have to co-sign for any college loans in order for such college financing to be approved.
Even with mortgages, lenders are not allowed to discriminate against you as long as you are 18 or of legal age to sign a home loan contract in your state. Again, though, in practical terms, very few 18-year-olds will have the assets or credit required to get a mortgage on their own.