Yes, in fact, GPS receivers are used constantly by pilots for navigation. There are a few caveats of course -- for one, GPS signals may not be at a high enough level inside an aluminum aircraft, due to aluminum metal shielding of the RF signals. Second, the number of GPS satellites that your receiver can see may be limited by atmospherical conditions present, especially at differing altitudes -- in practice, this will usually only reduce GPS accuracy to around 30 meter accuracy in some worst cases.

Also, consumer GPS devices will not work properly at extremely high speeds (higher than a commercial jet speed), as the government does not want this technology to be usable for missiles developed by other countries. A military-only GPS encoded signal does in fact work at such speeds for U.S. military applications.

I should caution you that receivers aboard with passengers are not permitted to be activated on commercial flights in the U.S.

One last caveat -- aircraft use precision altimeters and WAAS-enabled GPS receivers for accuracy; You should not expect comparable accuracy from most consumer devices.

I have gotten an older GPS receiver to work on a plane. I had to hold it against the window, so it could "see" the satellites, but it did work. I got Lat/Long & speed (550 MPH!).

I'm not sure if the GPS antenna in a phone is large enough to work on a plane.

No they are set to disable at certain altitudes

Only if the pilot lets you stick it to the windshield.

Sort of. The latitude and longitude would be a bit off due to the extreme elevation (the gps assumes you're on the ground), speed, and possibly interference. And no, you would not get altitude information.