There are three forms of hacker. There is White Hat Hacker, a Black Hat Hacker and a grey hat hacker.
A white hat hacker will often be someone who is working for a company to find exploits and security issues with the companies system. Any security issues will be passed on by the hacker to the person responsible for managing the system. A white hat hacker can also be someone who is hacking just for fun and a challenge without causing any damage or doing any malicious acts. They may even contact the person they have hacked to tell them about these security issues they have found.
A black hat hacker is almost definatly a person who is hacking with further intent of criminal acts. They will deface websites, steal data and perform many other malicious activities involving the data and information they have received via hacking.
A grey hat hacker is generally someone who performs a bit of both. They ofter do not perform extremely bad acts and may just deface a website rather than steal data and information such as credit card details, etc.
The motive behind hacking can often be more mischievous than sinister. For example: Someone may hack just to prove that they can.
Example invovling white hat hacker
Someone: "This is the most secure system we have to date, hard for any hacker to hack."
Hacker: "I'm sure i can find something wrong with it."
Someone: "Theres no chance."
Hacker: "Okay, i'll proove it."
Hacker: *Goes of and hacks the system*
Hacker: "Told you it is probably possible."
Someone: "What security issue did you manage to find?"
Hacker: "Well this is what i found..."