Philadelphia's Center City (bordered by the Delaware and Schuylkill rivers from east to west, and from South St. to Spring Garden St. from south to north) is quite safe, especially in the high-traffic areas of Old City and along Walnut Street and Rittenhouse Square.
Still, it is a city: Be aware of others around you; keep handbags zipped and secured; don't leave belongings alone in a public space; when in a cafe, bar, shop, or museum, do not leave anything you'd like to see again on the ground, on your table, or otherwise unattended. Pay attention to your surroundings, especially after dark on quiet streets, and in emerging neighborhoods such as Graduate Hospital, Northern Liberties, and the Italian Market area. If it's late, spring for a cab -- or, at least, don't walk alone. Please, please don't walk by yourself at night while talking on a cellphone -- or listening to headphones.
Crime tends to increase in times of economic strife, and petty crimes increase at the year's end. On a (somewhat) more positive note: The city's whopping homicide rate is generally not because of the untimely departures of out-of-towners. (But you might want to hedge your bets by not wearing a Dallas Cowboys football jersey or a New York Mets baseball cap.)
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.