Although the OP, ibex333, did not specify, there are basically two different strategies to play with refilling, and beyond that, depending on printer technology, two basic different types of printheads.
On most lexmarks and HP's, the printhead is a cheap foil strip on the cartridge and covered by a patient almost impossible to replicate. Either you refill the original cartridge or some commercial outfit with far better equipment does it for you. Even if the refilling process goes perfectly, eventually cheap foil printheads not designed to last burn out or clog.
On most Epsons, Canons, and Brother inkjets, the printheads are separate and of much higher quality designed to last. The cartridge itself is more accurately regarded as an inktank, and as such, can be either refilled with your own supply of non OEM ink, or its dimensions can easily be duplicated, and its cheap and possible for a third party to sell you a totally new inktank filled with their brand of non-OEM ink. The giant danger, as vsfoxe points out with any non-Oem ink, is to get something that clogs your very expensive printhead because the ink isn't formulated correctly. And with Epsons and not Canons, its very hard to get at the printhead to clean it, so taking a chance on a pig in the poke manufacturer can be an expensive mistake, and that is further complicated by the fact that many such third party outfits change their suppliers of ink all too often, they just make the inktank, and buy bulk ink from someone else.
Beyond that, all OEM inks are slightly ahead of generic inks on permanence and resistance to fading, but some generic inks feed every bit as well and sometimes better than OEM inks. Beyond that, at least for the photoprinting set, is the even trickier aspect of exactly duplicating the color balance of OEM inks. Not all that critical if you are just printing text or plain paper color, but really critical in photos.
Since printer manufactures now make their money on their OEM cartridges and not the printer itself, they try to get you to suck in on buying a cheap printer knowing they will eat you out of house and home on the
replacement cartridges costs. And now we have chips to worry about as the refilling game gets harder.
To give you an idea of ink mark ups, about the cheapest you can get ink in OEM cartridge form is about $2600.00 a gallon ( gallon unit arbitrary ) And that is cheap because many charge well over $10,000.00 a gallon. Yet they can make that ink for less than $50.00 a gallon. As a consumer you can get some top quality inks generic inks retail for less than $150.00 in far less than gallon units and save a bundle. And refilling my non-chipped Canon is very easy. 8000+ pages and still going.