PARENTS - Jack "Siddor" Barrett and Queen Paté
SIBLINGS - Anna Galena Barrett
'GRANDCHILDREN' - Susan 'Foreman'
PARTNERS - Midge Cartwright (briefly), Caroline Burnholme, Sarah Michelle Gellar, Queen Jane of Algor? Possibility of many other "companions".

Jim Barrett is a time-lord. Well he's half time-lord, maybe.
Jim has assumed the following incarnations:

1 - William Hartnell
Jim's early years are shrouded in mystery. He may have had inarnations before this but it is now generally accepted that he didn't. There are those that suggest that Jim was in-fact "The Other": one of Gallifrey's founding fathers. There are also suggestions that Jim is a hangover from a previous universe, and that he created the Timelords for somewhere to hang out. Some even say that Timelords are part vampire, though presumably Jim wouldn't've lasted long with Sarah Michelle Gellar if that were the case. More commonly suggested is the idea that Jim was "loomed" to a Timelord clan, possibly called Lungbarrow. But all of these notions seem to be invalidated by the simple fact that we know who Jim's parents are.
Anyway... he was brought up by his Uncle Egbert, and educated on Gallifrey, only to get thrown out of college there. Fed up, he split in a stolen Tardis, and under the alias "The Doctor", he managed to aquire a grand-daughter. He also did a lot of good work for charity but eventually he wore out his body and was forced to regenerate as:

2 - Patrick Troughton
In this incarnation he was a much more cheeky soul and made a minor nuisance of himself across the universe. But the powers that be got fed up, and locked him on Earth in the body of:

3 - Jon Pertwee
Which was all a little embarrassing to be perfectly honest. He got involved in an X-Files kind of set-up and Jason Kinged his way around the UK in a dodgy old car. Eventually he died and became:

4 - Christopher Eccleston
Who eventually found himself in York with the Earth held hostage by geese. Here he met two future versions of himself. They went up to Central Hall (a space ship) where he got chopped up a bit and was forced to regenerate as:

5 - Frank Skinner
All was fine for a while and then he got blown up a lot. But fortunately, a future version of himself went back and altered things. So forget the last two entries. The real truth is that Jon Pertwee regenerated into:

4 - Christopher Eccleston
Who eventually found himself in York with the Earth held hostage by geese. Here he met Stew Jester and Leon Protznedvic, and the three of them took the Tardis to the Barbican (a space ship) where they avoided death as the Earth exploded down below.
After this brief incident, Jim decided that the years as Pertwee had made his brain soft, so he went back in time to 1985, only to wind up with his Tardis stolen. After twelve undocumented years (during which it's possible that Jim sustained some memory loss), he enrolled in university again. Here he met up with Stew Jester and Leon Protznedvic (again) along with Alex Jefferson who he'd met at the Barbican. But this was in the past, so they didn't know (such are the rigours of time travel). Then they all died in an explosion, but before he had time to regenerate, Jim was reanimated by MI7, who very kindly gave him a job as a compsci.
He was just settling down in this career when he was hurled into a parallel dimension. Here he met Omra, his father's old mentor. Omra taught Jim in the Power of Greyskull, and then Jim accidentally killed Omra. For this he was arrested and sent to a prison planet where he was reunited with his university friends. Together they escaped only to wind up getting sucked into the television.
From there things got worse, and they ended up in TV Heaven, before finding an escape route. Just as they were about to leave, Jim got kiled and was forced to regenerate as:

5 - Frank Skinner
And then he and his friends headed out into TV static before winding up hypnotised by an evil Fred Harris's Chocabloc. Fortunately they were saved and were able to return home again but not before nearly getting killed by Siddor.
Jim and his colleagues returned to their realty, but not before creating an alternative reality inwhich they found themselves on the high seas, and inwhich Jim eventually committed suicide as a result of Caroline's excessive quoting of Eddie Izzard. It seems his attempt was unsuccesful however, as he cropped up in the EDS office later.
It was around this point, in the real reality, that Jim found out that Siddor was actually Jim's father. It was also around this time that Siddor took over Jim's favourite pub, and threatened to kill Jim and his friends.
Jim had no choice but to fight his father in a battle of logic. But he lost.
So he and his friends sought the help of two ancient super heroes, and this time they won, but not before getting killed.
Jim now found himself in Hell. Quite why he ended up properly dead remains something of a mystery. Maybe he was not prepared for the death and so was unable to regenerate in time. Or maybe Stew had pulled some strings in his temporary capacity as ruler of Hell. Probably the latter or a combination of both.
Anyway, Jim remained in hell until some rogue geese held the Earth hostage. Then Jim was allowed out to help save the world. During this escapade, he got pecked to bits and had to regenerate again as:

6 - Tom Baker
And all was well for a few minutes but then he got blown into several pieces. Fortunately he was able to regenerate again as:

7 - Anthony Head
But unfortunately, his new body was severely damaged by too long a time spent in the vaccuum of space. So again he regenerated, this time as:

8 - Peter Davison
In this body he found that people confused him with Rod, Lord of Magor. This was a minor inconvenience, but he put it to the back of his mind and resolved to go back in time and try to save the Earth again. So he went back in time and met several previous versions of himself (which is always rather confusing), and managed to get them all in the Barbican (which was a spaceship) and off the Earth. Then he disappeared in a puff of logic because he'd rescued version 5 of himself before he got chopped up. So:

5 - Frank Skinner
Is alive and well and in the Barbican when he gets splattered in a Tardis accident and so becomes:

6 - Tom Baker
Right. He goes off across the universe again, perhaps with Alex Jefferson, and gets into all sorts of hilarious scrapes. Eventually he returns to York with Sarah Michelle Gellar, and with no recall of the geese situation.
Here he meets two past versions of himself and they all go off to Central Hall where he gets shot and so regenerates as:

7 - Anthony Head
And then he gets blown up again, but fortunately, a past version of himself has already corrected this loop (as you will already have read) and so what actually happened was that:

6 - Tom Baker
Returns to York with Sarah Michelle Gellar and meets two past versions of himself. The three of them go to the Barbican which is a safe distance from the exploding Earth. But then he gets crushed by some seating in the Barbican and has to regenerate as:

7 - Anthony Head
He and Sarah then have to rescue two colleagues, Babysham and Alan, after they get trapped in a stargate.
They try to settle on Planet Musaka, but decide their community needs more women and so they head to Planet F34 where they meet another future Jim.
They return to Hell where Sarah is sectioned, and our Jim sets up a computer shop: Barretts of Harrogate. While in this job he is called out to reprogram Babysham, but is hypnotised by the goddess Bhuvana. As a consequence, the reprogramming job he delivers is slightly sub-standard.
Anyway... at some point he regenerates as:

8 - Peter Davison
Who goes off on various adventures dressed as a cricketer, and may or may not actually be Rod, Lord of Magor. It is certainly very possible.
If he is Rod, then he finds himself as a Nordic god, and presumably not a very good one as he keeps having to carry out tasks to maintain his godly status (finding the Crystal of Enderon, completing the Twelve Tasks etc). His rival as a Nordic god is Jane of Algor. Eventually, it seems he loses his godly status, as does Jane, and the two of them join a band called Gatherer's Moon.
If he isn't Rod then you can ignore that paragraph.
Anyway, he ends up on F34, where he isn't very well. So he regenerates as:

9 - Steve Davis
What he gets up to in this incarnation is unclear. At some point he finds himself in Hell, pursuing Leon after the assasination of the Gods.
Anyway, simple maths tells us that eventually he regenerates as:

10 - Colin Baker
During which time he is unstable and a bit crap. Fed up with this he becomes:

11 - Sylvester McCoy
Who is also moderately crap and has to do battle with some really naff adversaries. Then he gets shot in America somewhere and winds up as:

12 - Paul McGann
And rides around on a motorbike having lots of fun. And that's the last we see of him until he regenerates again and goes all evil. Maybe.