Your printer ink cartridges play as big a part in the final quality of your print as the paper that you use. If you use cheap paper, your print quality will suffer and in many cases the same is true of using cheap ink cartridges. This isn't always the case, however. Discount ink can be bought in a few different ways and each of them has advantages and disadvantages.
The first option for cheap ink is to refill your empty cartridges. This is generally the cheapest of all the alternatives, but it is also tends to wind up with the lowest quality prints.
It'll depend on what brand and model of printer you have, but many of the newer printers are difficult to refill. It can also be quite messy because you're dealing with bottled ink, trying to inject it back into the empty cartridge.
There are plenty of companies that recycle cartridges for you. They basically take the empty cartridges, clean them up, refill the ink and test them.
This is more expensive than refilling your own because you're paying for the labor involved, but it tends to give you better results.
These companies have refilling and cleaning equipment that can do a much better job of remanufacturing your empty cartridge. They also generally offer a guarantee on their work, so if the cartridge doesn't work properly you can either get a replacement or get your money back.
Generic Brand Cartridges
Generic cartridges are not as common as the other two options, mainly because many printer companies have patents on their ink cartridges so no other companies can duplicate them.
There are some cartridges that you can find brand new generic replacement ink for. These generic cartridge are not recycled, they are new but they aren't made by the printer companies themselves.
These cartridges tend to be the highest priced of the three options, but they are still cheaper than the original cartridges, and work just as well.
Which option will be best for you is going to depend a lot on how much printing you do, and what you're printing. If you're printing photos that you want to be able to keep for a lifetime, you'll have different needs than if you're just printing copies of web pages for future reference.