I presume that you are comparing these in case of using them in noun form.
1. aim is used when there is an obvious, visually or psychologically, target or direct link/line between where you are right now and where you want to go.
2. purpose is used in general case and the final target could be ambiguous and philosophical.
3. intent is more a combination of both mental goal and the process in between. Intent is mainly used in legal and literal. Also, only the object, such as human or its action, with "mind" could have purpose and intent.
4. My SAT scores are 2400 and my aim is to reach 2000 by the end of my junior year. It is not typical to use "intent" nor "purpose".
5. The purpose of my life is to bring peace to the world. Aim is not good for this case and intent is too "out of the body".
6. The attack was planned with intent to kill. Using purpose here is ugly.
2012-01-10 12:38:01 補充：