I have managed to get 4855 points in... Kestrel!
(I can post some screens if you want.)

So far I have played 338 times, some eneded fast (1st / 2nd jump) in others boss was little challenge.

I have won at least once each ship, and I didn't manage to get only 3 achievements ("disintegration ray", "clash of the titans" and "BOARDING OBJECTIVE SUCCESSFUL").
I'll try to do them in this week, and then check some mods.

And how are you doing? :)

The best I have is 6376 in the rock cruiser Shivan. This is with normal playing. Note that it is unfortunately possible to use the rebel fleet to inflate your score. Just cruise through the compromised sectors and each ship defeated gives 25 points or so. I have seen scores up to 8000 pointsfrom people who did that.

Heh, and I thought my score was good...

But jumping through rebels just for score - questionable, in my opinion: no loot, so only risk.

I did 5488 with The Osprey during normal playing, but never hunted for highscores. Would have been more, if i'd found the secret sector in this playthrough.

At one point I set for myself the goal of fully upgrading my ship by the end-boss. I got within 1 or 2 upgrades one time but never made it. In any case it was obvious I needed to optimize for scrap or loot if I ever wanted to achieve this. So for a whole lot of games I would try and hit as many beacons as possible at all sectors, even if it meant fighting 1 (or rarely 2) rebel ship on the way back to the exit beacon.
My highest score comes from using the Engi cruiser with this method and also on that run I used it as an asphyxiator with the ion weapon, asphyxiating crews while I got enough crew and scrap to build an invading party. I got 6303 points on that one.

Is it just me or does anyone else think that beating the flagship at the end should actually add something "special" to your score? I have a bunch of (admittedly older) high scores where the high score was from a game that didn't defeat the flagship (due to me doing something stupid no doubt), while the scores underneath all did defeat it.

Also the fact that you can inflate your score by wasting rebels endlessly (or until you screw up and need to repair) is a bit dodgy too... Kind of makes the high scores almost meaningless...

Well, it adds a shiny 'victory' label, which is satisfying enough for me ;-)

Also, unless you disable the Fleet pursue via a mod, you can't really waste rebel "endlessly", so it's a fair risk vs reward proposition.

Highscores weren't attractive to me either. I found the statistics and unlockables more satisfying.
Anyway, does anybody know the algorithm for the final score, it's probably deducible from the actual stats.

Think you misunderstood how it works. You fight through the sector for extra "ship defeats" only once the rebel fleet controls all of it, not before. Sure its not endless, but you can defeat one ship at each beacon, that would be what, 20 beacons per sector. Each rebel pursuit ship gives another 25 score, so you can have an additional 500 score per sector. Its probably too risky to do this in S1 and 2, but in sector 3 my ships is usually good enough to defeat the rebel ships easily.
So take a normal score of 6000 and you do this in 4 sectors, thats then 8000 score.

@DeMignon Yes someone posted the breakdown somewhere, its like 25 points per ship defeat, 10 per beacon explored and so on. (not exactly sure about these numbers)

Yeah, quoting directly from http://ftl.wikia.com/wiki/Score:

Score = (s+10*b+20*d)*D

s = scrap collected. Initial scrap (30 on easy, 10 on normal) and scrap gained by selling at stores does not count toward this total.
b = beacons visited
d = ships defeated by reducing hull or crew to zero
D = difficulty modifier, 1 on easy, 1.25 on normal

AFAIK this is correct.

As an aside, I would have liked for the game to keep a list of all the crew for each ship that's displayed in any of the high score tables, also including those crew that fell in the line of duty. That way it would be easy to tell which one actual crew-member (and from which ship) actually got that "most evasions piloted" score. Not a big thing and wouldn't change the gameplay at all, but I remember some ancient sims (where crew were involved) having this kind of feature and reckon it would be kind of cool.

They should also include those guys who were on the "winning" ship at the end, but didn't survive to the victory ceremony (so to speak).

Thanks for the algorithm.

You're right, tracking of crew members would've been nice! I always used to name them individually and would love to see them again in the statistics.

3981 on Easy with the Nisos