Notoriety is fame you get from doing something bad or being part of a misfortune or scandal. Just remember: Notoriety's not al-righty. Charles Manson earned notoriety for his grisly crimes.
In our celebrity culture, it's hard not to think that seizing your 15 minutes of fame is worth the shame of earning it through stupidity, scandal, or evil. (See: people's motives for going on reality television.) We ordinary mortals can comfort ourselves with the knowledge that most people who become notorious fade from the public mind quickly.