Since you mention P3200 specifically, and to expand a little on what Donald said:
When this T-MAX P3200 first came out, a lot of people submitted it for printing with exposures at ridiculous ISO and developer combinations. So I had the lab I worked at post this section of the Kodak technical information bulletin at the drop-off desk.
"KODAK T-MAX P3200 Professional Film is specially designed to be used as a multi-speed film. The speed you use depends on your application; make tests to determine the appropriate speed.
The nominal speed is EI 1000 when the film is processed in KODAK T-MAX Developer or KODAK T-MAX RS Developer and Replenisher, or EI 800 when it is processed in other Kodak black-and-white developers. It was determined in a manner published in ISO standards. For ease in calculating exposure and for consistency with the commonly used scale of film-speed numbers, the nominal speed has been rounded to EI 800.
Because of its great latitude, you can expose this film at EI 1600 and yield negatives of high quality. There will be no change in the grain of the final print, but there may be a slight loss of shadow detail. When you need a higher speed, you can expose this film at EI 3200 or 6400. At these speeds, there will be a slight increase in contrast and graininess with additional loss of shadow detail. (See the processing tables for adjusted development times.)"
and
"You can also expose this film at EI 400 and obtain outstanding shadow detail. See the processing tables."
http://www.kodak.com/global/en/professional/support/techPubs/f32/f32.pdf
Obviously some developers will give you a higher working EI, and some of those have been mentioned in this thread. Just don't expect it to be a 3200 ISO film without special treatment, increased contrast from "pushing", and/or loss of shadow detail. As the instructions say, it's 800 ISO with standard developers. The speed implied by the P3200 name is marketing.
Lee