Well, apparently, if we are of the opinion that he came out of a loom looking like 56-year-old William Hartnell (but can work even if the First Doctor was not always old):
(ages may contradict what said in the series, but they're not necessarily strictly chronological as the Doctor follows a different wiew of time, plus i'm being a bit AU)
The First Doctor steals the TARDIS as a 95-years-old, after having been a teenager for 50 years. He runs away with his "granddaughter" Susan (which is just another Timelady named Arkytior or the Lady Larn, that regenerated to look like a toddler)
We first see the Doctor as a 110-years-old, and Susan as a 15-years-old. (Susan aged like an human because she was chameleon-arched and wanted to be an human teenager. At this point, the Doctor does not like humans very much, though.)
When the Doctor leaves Susan, the Doctor is 113, and Susan is 18. Ian and Barbara never age past the ages they both were in 1963, they're both around 40 but still look 37.
115-year-old Doctor and 42-year-old Ian and Barbara, join up with Vicki Pallister, who is currently 16.
43-year-old Ian and Barbara get replaced with 35-year-old Steven. the Doctor is 116, and Vicki is 17.
Vicki leaves the show at age 19 to get replaced with the 16-years-old Dodo. Steven is 37, and the Doctor is 118.
39-year-old Steven and 18-year-old Dodo get the boot of the replacement, new companions being the 34-year-old Polly and Ben. the Doctor is 120.
The Doctor regenerates for the first time at 122-years-old, Polly and Ben are 36. 25-years-old Jamie joins the crowd.
Polly and Ben get the boot when they are 38, and replaced by 18-years-old Victoria. The Doctor is 124, and Jamie is 27.
125-years-old Doctor, and 28-years-old Jamie, when they're joined by the 15-years-old Zoe.
The Doctor is 129 when he gets changed into the Third Doctor and works at Unit. 32-years-old Jamie and 18-years-old Zoe get their memories cancelled.
The Doctor is around 129-132 while in "series 6b", 132-years-old working with 26-years-old Liz, then he meets Jo when he's 133 and she is 23. They split off when he's 139 and she is 29.
141-years-old Doctor meets 26-years-old Sarah Jane. The Doctor regenerates into Fourth when he's 145, Sarah's 30, and new-comer Harry is 32.
146-years-old Doctor and 31-years-old Sarah leave a 33-years old Harry. The two enbark in many adventures, until 153-years-old Doctor has to leave 38-years-old Sarah.
The Doctor spends a little bit on Gallifrey alone, as Lord President, from 154-years-old to 159-years-old. Then he meets the 6-years-old K-9 and 23-years-old Leela.
Leela leaves the Tardis as a 27-years-old, and the Doctor is 163-years-old.
164-years-old Doctor and 148-years-old Romana, who regenerates for the first time at 149.
172-years-old Doctor and 156-years-old Romana welcome 14-years-old Adric in the group.
157-years-old Romana gets replaced with 16-years-old Nyssa. The Doctor is 173 and Adric is 15. 23-years-old Tegan also joins in a few months later.
The Doctor regenerates into Peter Davison at the age of 174. Nyssa is 17, Adric is 16, and Tegan is 24.
Adric dies a few months before turning 17.
20-years-old Nyssa gets replaced with 24-years-old Vislor Turlough (tho he's posing as 14). The Doctor is 177, and Tegan is 27.
Kamelion is 3 by the time he is in the TARDIS, but only stays here for a few months.
28-years-old Turlough finds 18-years-old Peri, who stays in the TARDIS. The Doctor is 181, and a few days later he regenerates into Colin Baker.
The Doctor and Peri tag along until the Doctor is 184 and Peri is 21. She gets replaced by the 22-years-old Mel Bush (who had previously been a companion of the Seventh Doctor from her side of things), and a few months later, the Doctor regenerates into Sylvester McCoy.
The 185-years-old Doctor leaves 23-years-old Mel for 16-years-old Ace McShane, who remains in the TARDIS until she leaves for the Time Lord Academy at the age of 20, and The Doctor is 189.
The Doctor is 192 at the time of the TV Movie, and the Time War begins when he's 198.
The Doctor becomes The Warrior (John Hurt) at age 199, and stays in this form until age 219, when the sullness of being war-torn ages him a lot, and the last bullet from the Time War turns him into Christopher Eccleston.
The Doctor is 219 when the New Series starts, having only spent a few months in his ninth (tenth if you count Warrior) body. He meets 18-years-old Rose Tyler, and 21-years-old Adam Mitchell, and the 42-years-old Jack Harkness (even tho he gets revived by the Tardis and cannot age anymore, like Barbara and Ian but explained better.) also are in for short rides.
The Doctor regenerates into David Tennant when he's 220 and Rose is 19.
The 223-years-old Doctor leaves the 22-years-old Rose Tyler with his hand-clone, and then meets Martha Jones when he's 224 and she's 28.
The 227-years-old Doctor replaces the 32-years-old Martha with the 43-years-old Donna.
The Doctor regenerates into Matt Smith when he's 232, and starts travelling with the 21-years-old Amy and the 20-years-old Rory. He also gets mysterious visits from the 51-years-old River (which we know, is actually the Tardis-conceived future daughter of Amy and Rory). The 237-years-old Doctor leaves the 26-years-old Amy and 25-years-old Rory for the 23-years-old Clara.
The 238-years-old Doctor goes away from 24-years-old Clara to protect Trenzalore until he's 245-years-old and has picked up the 83-years-old Cyberman Head: Handles. Then, he regenerates into Peter Capaldi.
... And the legend lives on, as the 246-years-old Doctor, 84-years-old Handles, and 25-years-old Clara pick up the 34-years-old Tom, the Coal Hill teacher. Handles explodes less than one year after, in a particularly contrived adventure. The 18-years-old Jenny, loomed daughter of the Doctor, joins in as a Susan surrogate. And they meet both new and old friends, filling many hearts and bringing peace. NuWho gets cancelled in 2030 and changes its name into "Doctor Who Part 2", with a "Part 3" returning in 2038, thriving until the 100° Anniversary in 2063, where he breaks the 4th wall to say "goodbye", and makes one of the best flashback scenes ever.