The Third Doctor was a suave, dapper, technologically-oriented, and authoritative man of action, who not only practiced Venusian Aikido (or Karate), but enjoyed working on gadgets and riding all manner of vehicles, such as the Whomobile and his pride and joy, the canary-yellow vintage roadster nicknamed "Bessie," a construct which featured such modifications as a remote control, dramatically increased speed capabilities and even inertial dampeners.
While this incarnation spent most of his time exiled on Earth, where he grudgingly worked as UNIT's scientific advisor, he would occasionally be sent on covert missions by the Time Lords, where he would often act as a reluctant mediator. Even though he developed a fondness for Earthlings with whom he worked, he would jump at any chance to return to the stars with the enthusiasm of a far younger man than himself. If this Doctor had a somewhat patrician and authoritarian air, he was just as quick to criticise authority too—having little patience with self-inflated bureaucrats, parochially-narrow ministers, knee-jerk militarists or red tape in general. His courageousness could easily turn to waspish indignation. It is thus no surprise that a common catchphrase of his was, "Now listen to me!"
Despite his now-and-then arrogance, the Third Doctor genuinely cared for his companions in a paternal fashion, and even held a thinly-veiled but grudging admiration for his nemesis, the Master, and for UNIT's leader, Brigadier Lethbridge-Stewart, with whom he eventually became friends. In fact, even when his much resented exile was lifted, the highly moral and dashing Third Doctor continued to help UNIT protect the Earth from all manner of alien threats.
In general, this incarnation of the Doctor was more physically daring than the previous two, and would confront an enemy physically if cornered. This often took the form of quick strikes, with the occasional joint lock or throw - usually enough to get himself and anyone accompanying him out of immediate danger - but usually not to the extent of a brawl, in keeping with the Doctor's non-violent nature. He would only use his fighting skills if he had no alternative, and even then generally disarmed his opponents rather than knock them unconscious. Indeed, his martial prowess was such that a single, sudden strike was usually enough to halt whatever threatened him, and at one point he reminded Captain Yates (physically as well as verbally) that Yates would have a difficult time removing him from somewhere when he did not want to be removed.
Perhaps due to his time spent on Earth, or maybe just as a function of his pacifistic and authoritative tendencies, the Third Doctor was a skilled diplomat and linguist, as well as having an odd knack for disguises - all of this, combined with his formidable galactic experience, often allowed the Third Doctor to play a central role in the events he found himself in.