While it is always preferable to have a dedicated set of track wheels and tires, that is not always practical for every driver that ever sees track time. Drivers who go to the track very infrequently may not be ready to commit to having a second set of wheels and tires for the track.
If you do choose to run your street tires on the track, make sure to inspect them carefully before you go out. A small injury to the tire that might not cause a problem in daily driving could have a much bigger effect at the track.
Also, make sure to drive within your limits if you plan to continue using your street tires after the track day. Sliding through corners is fun, but it can easily destroy a set of street tires in one day of lapping. A clean, smooth line can be equally fast and leave you with tires that are still usable.
If you are buying street tires with occaisonal track use in mind, consider an Extreme Performance Summer tire. These tires are engineered with the possibility of some track duty in mind, and will hold up better than normal performance tires.