Hacker has a variety of connotations. Media commonly use the words hacker or hacking in association with malicious computer break ins. However, these words have a much richer history. (See the references below for a variety of views and perspectives on this matter.) Among computing professionals, "hacker", "hack", and "hacking" denote creativity, inventiveness, passionate curiosity, and the ability to think and work outside of normal parameters. This later tendency sometimes manifests itself in unauthorized system penetrations. However, in the more classic usages of the word hacker, such hacking is motivated primarily by technical challenges and a sense of discovery, not by any malicious intent. Hackers are often categorized with descriptive adjectives. The most widespread of these include:
A white hat hacker is a security professional who performs system penetration testing under contract. This usage is reflected in the Certified Ethical Hacker (CEH) certification standard offered by the EC-Council.
Black hat hackers are indeed malicious (or at least entirely self-interested). Common black hat activities include theft, vandalism, or espionage.
Gray hat hackers have motivations similar to the classic definitions of hacking. Namely, gray hats are mostly curious, but they may be willing to transgress various regulations and other barriers in the name of personal research. Sometimes gray hats report any vulnerabilities they discover to system owners or other authorities, who may or may not appreciate the unsolicited security testing.
Script kiddie is a word of derision applied to amateurs using tools provided by other, more sophisticated hackers. Thanks to widespread code and software distribution over the Internet, powerful penetration tools are freely available to those with little system knowledge or understanding. Script kiddies are those who wield such tools with a minimal personal skill set.
Cracker is essentially synonymous with black hat hacker. Sometimes the word cracker is used when the author wishes to form a contrast with the more positive connotations of the word hacker.
Hackivists use system penetration tools in the name of a cause. Hackivists may exfiltrate private or classified data and publish it to the world. They also often deface web sites or perform denial of service attacks against targets they oppose. Whether such hackivism is blameworthy or praiseworthy depends largely on the political sympathies of those assessing the hackivist's actions.
References:
http://paulgraham.com/gba.html
http://outspan.hubpages.com/hub/Meaning-of-Hacking-and-the-Different-Kinds-of-Hackers
http://www.cs.berkeley.edu/~bh/hacker.html
http://www.peterbe.com/plog/blogitem-040313-1
http://www.eccouncil.org/courses/certified_ethical_hacker.aspx