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By the time of Pyramids of Mars the Doctor is about 750 years old. In The Tomb of the Cybermen he tells Victoria that he's 450 Earth years old (Since Gallifrey's other qualities are Earth like, and since the Doctor continually boasts of his age to humans, we might assume that there's not much difference between Gallifreyan and Terran years).
The difference between the two figures might in part be explained by the long period that the second Doctor spent travelling (often on his own) after the trial (see The War Games). (It is also possible that the Doctor spent a good deal of time wandering mid-Robot: see The Face of Evil.) He is 749 in The Brain of Morbius and The Seeds of Doom. He turns 750 before The Robots of Death, and has reached 759 (his vanity makes him say it's 756, but Romana knows better) by The Ribos Operation. After The Invasion of Time, therefore, he spent a few years wandering on his own.
He turned 760 before The Power of Kroll, but by The Creature from the Pit Romana is teasing him about his claimed age (750). In The Leisure Hive we discover that he's been rounding down in order to disguise his true age. (The gaps between stories on his own or without human companions (The Deadly Assassin/The Face of Evil, The Armageddon Factor/Destiny of the Daleks) therefore cannot be more than a year or two in length.)
By Revelation of the Daleks and The Trial of a Time Lord the Doctor is 900 years old. The gap is best explained by the two Time Lords having adventured together for many decades (say between The Leisure Hive and Meglos). (The only other explanation would involve super long life span for Nyssa between Time Flight and Arc of Infinity.)
The sixth Doctor adventures for over 50 years during and after The Trial of a Time Lord: in Time and the Rani the seventh Doctor gives his age as 953. The third Doctor twice indicated that he'd been around for several thousand years (Doctor Who and the Silurians, The Mind of Evil), but he was merely indicating the range of Earth history he'd experienced.
Romana, incidentally, is in no position to complain about the Doctor's vanity, since she admitted to being nearly 140 in The Ribos Operation, slimmed it down to 125 for City of Death, and only allowed herself to be her full 150 in The Leisure Hive.