Can you become a banker with out any college?
Yes, although it's extremely hard and to "make it" you'll have to strongly rely on luck, would not recommend trying to become a banker without any college, unless your dad or relative owns a bank which I highly doubt because you posted this question.
It does depend on the type of "banker" but generally all you need is a 4 year college degree. The best degree for this is a business degree. Within retail, corporate or investment banking there are many types of specialities such as relationship management, credit risk, treasury, accounting each speciality has its own certifications (CFA, CPA, CFP, CPB etc)
You do not "HAVE" to attend any college. To get into the industry you just have to be able to do the work. College is a great way of gaining the ability and skill. Any college that offers computer science is good if you want to become a programmer. Schools that offer "Game art and design" or similar is good if you want to become an artist for games.