How old are you? Whatever your age was at your last birthday? But what about time travellers? A simple today's date minus your DOB isn't going cut it. Some for a Time Lord, it is far more complex.
The Second Doctor
The Tomb of the CybermenThe Doctor claims to be "something like" 450, implying that the First Doctor was that age when he died, seemingly of old age.
The War Games
"The Time Lords are an immensely civilised race. We can control our own environment - we can live forever, barring accidents and we have the secret of space/time travel."
We later learn that Time Lords could regenerate 12 times, and since (as stated above) the First Doctor died of old age, it gives a theoretical age of 5,850 years. Sure that's not forever, but for a human being it's pretty close. It is suggested at other times that the Time Lords can grant extensions, so forever may be possible.
The Third Doctor
The Planet of Spiders
Although the Doctor was mostly stuck on Earth with little time or space travel and spent a lot of time with humans who seemed to age in roughly real time his age at the time of regeneration was stated to be 748. He had previously mentioned during this regeneration about being a scientist for several thousand years.
The Fourth Doctor
His age is mentioned a couple of times, usually seemingly in real time, aging from around 748 to 760.
The Sixth Doctor
Claims to have been 900 a couple of times.
The Seventh Doctor
Time and the Rani
Fellow Time Lord the Rani's lab's access code is her and ther Doctor's shared age of 953.