If your university has a Computer Science degree program, you should take a look at the requirements and offerings in that program. Some Computer Engineering or Electrical Engineering programs also have programming concentrations. Taking some additional math courses may be a good idea as well, as your math abilities will help you solve problems in computing, and vice versa.
Finally, don't overlook your liberal arts and social science classes. Taking some non-major classes is usually required, and these classes can help you develop your fundamental reading, writing, and speaking skills.