As of 2010, Ahsoka's fate following the Clone Wars is unknown. Since she's a major character in the current Clone Wars series, it probably won't be revealed until the end of the series in 2012 or 2013.
Yes, Ahsoka did survive the Jedi Purge. During the final days of Clone Wars and Episode III, she and along with clone commander Captain Rex were on a planet called Mandalore. The planet was being controlled by the sith Darth Maul and they were attempting to take the planet away from his control. Eventually, Palpatine executed order 66 but Captain Rex disobeyed that order and help both him and Ahsoka defend them selves. They decided to fake there deaths and go into hiding.