Signing up for Amazon Prime may have seemed like a money-saving move during the last-minute holiday rush. In 2014, it could be a budget buster.

Amazon announced last week that the $79-a-year program had a "record-setting holiday season." Prime members get free two-day shipping on eligible items, free streaming of 150,000-plus movies and TV episodes, and free e-book borrowing from a library of more than 475,000 titles.