Always, always assume that whatever you tell a reporter might wind up on the front page of a newspaper or as the lead story on the 5 o'clock news. You can't think that saying, "This is off the record" magically protects you from being quoted.
Going off the record -- or on background, or any of these terms -- is an agreement between the source and the reporter. If the reporter doesn't agree, you're still on the record.
Caution: These terms aren't universally used. Many reporters don't often use "on background" or "not for attribution," and it's not something that professors spend a lot of time explaining in journalism school.
Slate Magazine repeated a test that William Safire did years ago by asking Washington Post reporters what the various types of attribution meant. Reporters at the Post are among the finest around, and even they didn't entirely agree on what these various terms means. Be careful and talk it over with the reporter beforehand.
1) On the record
This is simple. Whatever you say can be used. You don't really say these words unless you go "back on the record."
2) Off the record
This is anything but simple, and it generates the most confusion with reporters.
Many journalists will treat this information as quotable but not attributed to you. If you say it, they're probably going to use it. You can't unring this bell, because re telling a reporter something juicy and secret, and they're going to dig around and find somebody else to confirm what you said.
Some reporters say they think "of the record" means they can't use it at all -- although you can bet they'll gossip about it with friends, family or coworkers. Other reporters, including Bob Woodward, treat "off the record" as "try getting this from another source."
I'd advise never using this. It's smarter to either (a) keep your mouth shut or (b) set the ground rules by saying it "on background" or "not for attribution" and making sure the reporter agrees on the groundrules before you spill.
3) On background
This is useful for explaining something complicated, whether it's a 500-page environmental reform bill or how a new contract for the No. 1 NBA draft pick would affect the Chicago Bulls cap space. A reporter needs to understand in order to write the story, but it'd be awkward to make the story quote after quote from sources explaining how things work.
On background lets a source be more candid and concise.
4) Not for attribution
This means a reporter can quote you -- just not by name.
You see it all the time when "Hollywood sources" say an actor is hard to live with on set, when "White House sources" comment on a story or "corporate executives" say they'll be announcing a hot new product soon.