As other people have given some great answers already about specific industries that are ripe for disruption (and indeed, I have given similar answers elsewhere myself), I will instead give you a way to see how we determine what those industries are.
First, you have to decide what your business purpose is:
Are you trying to solve a problem (and if so, is it an immediate one or one that is less pressing or more esoteric)?
Have you identified a “need” that you feel that you can fill differently or betterthan current offerings?
Are you interested in fulfilling “wants” – things that are not necessary for “survival”, but rather fall squarely in “providing comfort”? (If so, do you want to build upon something that already exists, or create something entirely new?
Look at your daily life, and the objects, processes, and applications that you currently utilize. Identify any pain points.
Look at the world around you. Observe inefficiencies that could be removed with a better process.
Ask your friends, family, colleagues for their pain points.
Once you have narrowed down to a particular niche, create a survey and start calling (yes, on the phone – or better yet, in person) people who are representatives of that demographic and ask them the same things – what would they most like to change about “x”. Don’t stop until you have at least200 answers.
There is your business.