"play eve free" was a search which brought several people to my previous post and I thought, hey, post idea.
People can buy game time codes with real money (two months for 37 dollars/euros IIRC). These time codes can then be converted into in-game items called PLEX. You get two of them for each time code you convert, each of which adds one month of time to the account of the person who uses it. Plex are commonly sold on the market by people who want to exchange real-life money for game money, and they cost around 360 million isk right now. This means that if you can earn 360 million isk in one month, you can play eve for free.
There is an efficiency issue, which is that in most first-world countries people earn enough per hour that it is more time-efficient to pay for the subscription. As an example, someone earning 30m/hour missioning would take 12 hours to afford a PLEX, while earning 5 dollars (or euros) per hour in real life it would only take three hours to pay for a one-month subscription. Of course not everybody can find a job in this economy, much less one which actually pays the bills and where they can change their workload on a whim, so plex are pretty popular.
So: In order to play eve for free, you need to earn enough isk each month to buy one plex per account. Since you are working for the ability to play, there is a strong incentive to maximize your isk/hour. For this purpose I will cover the earning potential of some basic careers and passive income methods, as well as suggestions for some advanced careers.
In highsec the two entry-level occupations are mining and running missions. Mining in highsec on a single account is said to be worth 7.5m/hour, meaning it would take 48 hours of work to earn one PLEX. Missions earn 20-40m/hour, at which rate it would take 9 to 18 hours to buy a plex.
There are other things to do in highsec, of course, but they are harder to get into and may require a significant initial investment. Trade and manufacturing are big ones, supposedly worth billions per month for those who know how to make it happen. Another thing to look at might be invention, but I am even less than familiar with this.
EDIT 2011-10-20: Incursions in highsec make 50-100m/h plus LP, and they aren't especially hard to get into.
Moving out to 0.0 the numbers get bigger. Manufacturing can still be done, and although the margins are a lot higher the volume is generally quite small. Belt ratting in 0.0 is worth 30-40m/h and running anomalies in a carrier or golem should be worth an easy 45m/h not counting faction spawns or escalations. At 45m/h one plex will take 8 hours of work.
With the recent spike in megacyte prices mining in 0.0 is now almost worthwhile again. A solo hulk mining arkonor in 0.0 makes about 25m/h, while a properly bonused hulk with a hauler alt makes twice that, meaning earning 2 plex would take 15 hours in either case. With two hulks and one hauler three plex would take 12 hours.
One thing which is worth a lot more in 0.0 than other places is exploration, which is what I do. An accomplished carebear doing exploration on 2 characters can usually make a minimum of 100m/h (8 hours for 2 plex again), but a single lucky drop can be worth a billion isk and an exceptionally good day can pay for months of play time.
Passive income can be used to supplement primary income, or at higher levels could actually pay for one or more plex per month. For mission runners datacores from research agents can earn an extra 70-ish million per month, and planetary interaction can be worth more depending on where you do it. Kirith I believe makes around 300m/month doing PI in a wormhole, and has written about that a bit. You can even make extra characters on one account for the purpose of passive income -- three characters each earning 70m/month from datacores and/or 300 from PI would surely help things along, though there is a skill point investment which would have to be made.