The type of car that you can take on a track day varies. The usual type of cars that attends our days are your normal day to day cars, such as Renault Clio's, Mazdas, BMW, to more exotic cars such as a Ferrari or Lamborghini.
There are certain restrictions that the car must meet to be able to attend on an own car track day. The two main restrictions are noise levels and whether or not the vehicle is open-wheel based.
All circuits have strict decibel noise limits that must be adhered to and any cars failure to meet or be below the level set will not be allowed out on track.
Certain circuits or organisers will not allow Radicals or race teams onto their events. This will be stated on the requirements section for the individual track day.
You can check the decibel limits for all circuits here.