Well, not really a contest. More of present your best ideas kind of thing. I'll provide 2 examples and see what others come up with. I expect to see a lot of old ideas dusted off and trotted out, and I'm hopeful for some new ones to show up.
Lets face it, Pathfinder's idea of an economy is a mess. Class abilities and feats can make a mess of the 'balanced' system the rules present where you aren't suppose to generate a profit with player ability. After all, this is a game about heroic adventuring, not economic dominance! So, of course there are going to be loopholes and exploits.
To me the quintessential exploit is a 1st level Gunslinger. Or more specifically, any character with the Gunsmithing feat. Each day you can make 1,000 gp worth of basic Ammunition for only 100 gp. Sold for half price that generates 400 gp in profit. Not bad for a 1st level character! (But seriously, what town uses 1,000 gp worth of ammunition ever day?!?)
Required Investment: 1st level character, 1 feat, 100gp = 400gp/day profit. Super efficient!
My second and last example will be a 7th level druid. How will this druid break the economy? By giving up his trusty animal companion and turning his back on the gods. He will take up Druidic Herbalism. While this does require a serious investment into Wisdom, there really are no other costs involved. The druid doesn't need any other feats, doesn't need to alter spell selection, doesn't need a certain archetype, doesn't need certain items or circumstances other than a merchant that will pay full price for concoctions like they were potions. Also the merchant will pay full price for potions created beyond the minimum level they can be cast at.
Lets sham together a 7th level Druid's wisdom modifier. Lets say you start at 20 wis at 1st level. +1 at 4th level. Spells that can be cast per day are:
1st: 4+2 2nd: 3+1 3rd: 2+1 4th 1+1 with the bonus spells from 21 wis.
The herbalist can create concoctions at 1 per minute for 'free' up to his wis modifier per day. 'free' is assumed to mean only the gold cost of creating a potion. That means 5 free potions...plus 2 if the druid casts Owl's Wisdom on himself. That leaves 3 2nd level spells, 3 3rd and 2 4th. Of course the druid can't make 4th level potions but the druid could prepare 2 3rd level spells in his 4th level slots.
Lets say the druid and GM agree the merchant will pay full price for concoctions that give benefits for being prepared at a higher level. So our druid makes 5 Cure Poison concoctions at 7th level strength each day. Then he makes 2 Barkskin potions at 7th level strength too.
25gp x 3rd level spell x 7th caster level = 525gp per Neutralize Poison
25gp x 2nd level spell x 7th caster level = 350gp per Bark Skin
(525gpx5) + (350gpx2) = 3,325gp per day in 'free' potions.
But wait, there is more! If the druid can get ahold of a +6 headband of wisdom he can make 3 more potions per day for free, and won't need to waste a 2nd level spell on boosting his own wisdom. He will also gain 1 2nd, 3rd and 4th level spell from the improved wisdom. That means 7 3rd level concoctions, and 1 2nd level concoction for 'free'.
That also leaves 4 2nd level spells and 6 1st level spells unaccounted for. Seems like a shame not to make more concoctions, right? Druidic Herbalists of 7th level can also make concoctions at half the cost of a potion, which means they can make and sell those potions for half of the profit from the free potions. For our example lets say the GM limits our druid to selling Cure Light Wounds concoctions of 5th level potency for his 1st level spells.
4 x 350gp x .5 for the Barkskin potions = 700gp
6 x .5 x (25gp x 1 x 5) for the 1d8+5 CLW potions = 375gp
Totalled up that is 4200gp for 8 Neutralize Poison potions (for free), 700 gp for 4 half profit Barkskin potions, and 375gp for half profit CLW potions. So 5,275gp per day from a 7th level caster. Raising the caster level will dramatically raise the profits since all of the 2nd level and higher potions are based on caster level for their profits, and more 3rd+ spell slots will result in half-price 3rd level potions being produced, for 1/2 x 3rd x CL x 25gp profits for those extra spells.
Also, eventually Wishes could be used to raise wisdom, as well as extra stat bumps from leveling.
Anyways, not bad for a 7th level that needs no strange circumstances to make a profit.
So, what have you got?
Planar binding Efreeti for free wishes is the original break-the-economy scheme. See also: chain-gating. Both predate PF and Golarion.
Pyramid schemes! Constructs you make follow your instructions, any means your constructs have of making money will pay off sooner or later. I think the 'Painter Mage' who creates Trompe l'Oeil is the earliest this can be made to practically pay off (and it can grow exponentially), but schemes with simulacra predate PF/Golarion too.
The false focus feat (or the blood money spell) and spells like bless water or masterwork transformation create money for nothing.
There are an infinite number of criminal schemes with high pay & risk but these may be outside the scope of what you're asking for.