The TARDIS force field was a force field surrounding the outer plasmic shell of a TARDIS. It protected the occupant(s) from harm (though it was far from invulnerable) and from the Time Vortex and other environments dangerous to its pilot.
The First Doctor, on Susan's advice, once redirected the force field's power to his ship's engines, allowing them to generate the thrust sufficient to escape the Tick-Tock World. (AUDIO: Tick-Tock World)
When the Second and Third Doctors faced Omega, they were forced to shut down the force field to travel to the anti-matter universe. When they travelled to the other universe, the Second Doctor's recorder had gotten trapped in the force field generator. As it was still made of normal matter, the Doctors sacrificed it and the generator to defeat Omega. With this victory, the Time Lords undid the Third Doctor's exile though he noted that he would have to build a new force field generator. (TV: The Three Doctors) Having grown fond of life on Earth however, he held off doing this for a while but an adventure with Ramón Salamander convinced him to do so and resume his travels. (COMIC: The Heralds of Destruction)
During his fourth incarnation, the Doctor reconfigured the force field of his TARDIS into a corridor through which he could safely traverse a vacuum. (TV: The Horns of Nimon) In his eleventh incarnation, he repeated this operation to permit River Song to transfer from another ship in space. (TV: The Time of Angels)
The Seventh Doctor used the TARDIS force field to expel the Timewyrm from Adolf Hitler's mind. (PROSE: Timewyrm: Exodus)
The Tenth Doctor sometimes took the shield down, at least once to listen the Music of the Spheres. This resulted in the Fifth Doctor's TARDIS to merge with the Tenth Doctor's, the Space-Titanic to crash into it, and a Graske and a time portal to gain access. (TV: Last of the Time Lords, Time Crash, Voyage of the Damned, Music of the Spheres)
While the force field of a TARDIS was traditionally immune to a Dalek gunstick, (TV: The Chase, The Witch's Familiar, Resolution) the Dalek Empire, at the height of their power during the Last Great Time War, developed the technology to disable the force field of a TARDIS. This left the TARDIS as vulnerable as whatever its outer plasmic shell was mimicking. (TV: Journey's End, AUDIO: The Enigma Dimension)
After the Last Great Time War, Jack Harkness and the Ninth Doctor wired a tribophysical waveform macro-kinetic extrapolator into the TARDIS to enhance or enable its force field. (TV: The Parting of the Ways)
Turning a TARDIS to "basic mode" deactivated its shield oscillators. When the Eleventh Doctor did so, as he tried to teach Clara Oswald how to fly the TARDIS, it left his ship vulnerable to the magno-grab of the Van Baalen salvage ship. (TV: Journey to the Centre of the TARDIS)
Due to clinging to the TARDIS doors after being locked out, the TARDIS extended its force field to protect Clara Oswald in the time vortex. (TV: The Time of the Doctor)
When the TARDIS was brought to the Dalek City as Davros was dying, it activated its Hostile Action Dispersal System to fake its destruction. Its force field however remained online, protecting the Twelfth Doctor and Clara from the gunsticks of Dalek control. (TV: The Witch's Familiar)
While in Montgomery, Alabama in 1955, Krasko, a rogue time traveller, tried to displace the TARDIS in time with his temporal displacement weapon, only to discover the force field was up. (TV: Rosa)
When the Doctor's first life cycle was drawn in the Void, the first nine, discounting the Eighth Doctor, extended the force fields of their TARDISes to reinforce the bowship that the Ninth, Tenth, and Twelfth Doctors were using. (COMIC: The Lost Dimension)