Chief Commissary Hanseatic's Favourite Trade Runs

1. Perishable is Good

Reps required: white or better with Bretonians, Corsairs, Bounty Hunters, Outcasts, Orbital Spa and Cruises. Hessians in white is an advantage in the Omegas, but no necessity. Bounty Hunters in red could be risky, as cruise disruptor missiles cause extra spoilage.

Starting at Planet Cambridge:
Buy Luxury Food for 160$.
Fly the trade lane to Battleship Suffolk halfway, then leave the lane and fly about 20k to the Omega 5 jumphole.
(If you don't know the position yet, toggle the map to patrol lane mode, and set a mark at the intersection on the right side of the system.)
In Omega 5, accelerate towards Cadiz Base and fly past it to Omega 41 jumphole (about 16k total).
In Omega 41, mind the radiation (will cause about 3000$ worth of repair damage. Do spend a nanobot if losing more than three squares of hull) and avoid the central star while flying towards Omicron Theta jumphole.
In Omicron Theta fly west of the sun towards Sigma 17 jumphole.
Sigma 17 has about 30k straight flight to the Sigma 19 jumpgate or the jumphole (about the same distance). If Samura is hostile, take the jumphole.
Sigma 19 has about 15k to the Planet. Fly around from the right and dock at pleasure cruiser Hawaii. Sell for 1600$ apiece.
You'll lose about 7-8 units to spoilage on an uninterrupted run.

Investment: 44,000$ buying at Cambridge, plus about 3000$ repair cost for radiation damage in Omega 41 and the clouds.
The sale yields 425,000 or more, meaning a tidy profit of about 380,000$ just for the first half of the trip.

Continue empty to Omicron Beta jumphole in Sigma 19. In Omicron Beta dock at Ruiz Base and buy Xenoorganisms for 100$ of omicron beta
Fly to Omicron Alpha hole (about 12k). In Omicron Alpha fly the 6k to Omicron Theta hole.
In Omicron Theta fly straight to Freeport 9 and dock there, sell the entire load (about 272 or 273 units) to repair the damaged one, and buy a full load for 400$ of omicron theta
Fly along the sun to Omega 41 Jumphole, and the entire course back as described above.
map of omega-41
map of omega-5
In Cambridge, accelerate towards the sun until you see the trade lane to Planet Cambridge. Dock at Cambridge Research station - usually with 269 units intact, and sell at 2000$ apiece.
map of cambridge system

Investment 28700$ (including replacement of 3 spoiled units at Freeport 9) plus about 3000$ repair cost.
Sale of 269 units yields 538,000$, meaning a net profit of 500,000$ for the back trip.
In total 880,000$ for one return trip.

2. Manhattan - Hokkaido

A pretty low risk contraband run for characters hanging out around Manhattan.
Buy luxury goods on Planet Manhattan for 180$ apiece. Fly through Colorado and either Kepler or Galileo, Shikoku and New Tokyo to Hokkaido system using the trade lanes, or if you are reduced to crawling the jump holes, fly through Colorado, Galileo, Shikoku, Kyushu and Hokkaido. Sell at the Golden Chrysanthemum base Ainu Depot for 1450$ and buy Cardamine for 420$ or so. Return to Manhattan, dodge the police, sell for 1500$. Alternatively deliver gate parts to Chugoku Gate Building Site in Hokkaido from Station Pueblo, Colorado. Net profit of the return run about 2000$ apiece.
Having white or better reputation with most of the pirates along the route helps, but isn't really required, except for GC. The greatest risk will be player pirates at Manhattan (or Rochester Station if police catches you smuggling in NY).

3. Diamonds are a Girl's Best Friends

An alternative to the Cambridge-Hawaii run

The usual advice to traders is "Buy diamonds at New Berlin" or "Buy in Dresden".
If you are sufficiently friendly with the Hessians, buy from them - that's how they finance their war on the Corsairs. They are the cheapest supply in Sirius, and one of the most convenient basis is Ronneburg in Omega 5, about halfway between the Omega-7 and Omega-11 jumpholes. 180$ apiece.
Go to the Omega-41 jumphole (carefully - there are mines just south of the Omega 11 jumphole), and follow the Hawaii run into Sigma 19. Continue through Honshu to New Tokyo and sell the diamonds there, for 1650$ apiece. Fly empty to Planet Honshu (there is only inconsequential profit to be made on this run) and buy engine parts there for 150$ apiece, continue through Sigma 19 to Ruiz base and sell the engines for 971$ apiece.

Afterwards, return with Xenoorganisms to Cambridge Research Station.

4. Arms 'n Artefacts

courtesy SP-Nightshade on the Freelancer Universe forum thread "The Ultimate Trade Route":
Buy Light arms from New london and go to Cadiz base thorugh leaving the trade lane halfway and taking the jump hole.
And on the return run buy artifacts.

That's about 800$ per trip and piece, without any radiation damage. Excellent for just two jumps.