Recently hacking has come to mean unauthorized access to data/information, to obtain or to modify it.
Previously, it referred to many things, usually related to a style of working that is either very good or carried out in a spirit of experimentation. When free software authours use the word, they usually mean the old meaning. See also The Jargon File
A group known as the "Hacker Antidefamation League", wish to restore the old meaning to "hacking", preferring the word "cracking" to refer to unauthorised access.
What are some methods that hackers use?
Since Hacking is the process of making a computer program work better, then any tools used by a system administrator or a computer programmer are part of the methods used used by hackers.
What have (some) hackers done to earn their reputation (unauthorized access)?
NO hacker ever engages in unauthorized access, so any reputation they receive is based on a misunderstanding by the public that a person who understands the details about how a computer works will use that knowledge to break into other people's computers. This misunderstanding is spread by crackers calling themselves hackers, and the press perpetuating the term.
Have there been some famous hacks?
There have been many wonderful hacks, emacs is one example. I doubt many of them are famous, however, because noncomputer people rarely understand exactly what makes a hack famous. To be famous, a hack must show a high degree of novelty, as well as a deep understanding of the way computers work, and must be significantly more elegant than a kludge.
I ask these questions because I'm concerned that the above is just like an entry in a dictionary of usage, and Wikipedia isn't a dictionary of usage, it's an encyclopedia.
What are some methods that crackers use? Some recent crackers have sent programs in email to unsuspecting users as attachments. Running these programs will give the cracker access to the computer. The programs can be classified as worms, virii, and trojan horses. They work in different ways, but mainly they become zombies to the person who sent the original email. After recruiting these zombies, a cracker can remotely command them to attack other computers to take them over, more zombies, or overload a computer that can not be taken over (Denial of Service attack). It is generally thought that crackers do this to be noticed by their peers.
Have there been some famous cracks ?
Definitely. The Morris Worm is famous, as the first worm that went out of control and slowed much of the Internet of its day to a crawl. It had no payload, but simply tried to reproduce, which it did in an uncontrollable manner.
This page should probably be combined with hacker.