Brand Name Ink Cartridges
Companies like HP, Canon, and Lexmark have built multi-billion dollar businesses around printer ink cartridges. They often sell inkjet printers at cost or even at a loss, knowing they will make their profit from the ink.
Unlike some people, I don't think Epson, Canon, and HP are evil. They are in business to make a profit, and the profit is in inkjet cartridges. But that doesn't mean you have to buy their printer ink. It's simply one of your options.
So why buy an Epson inkjet cartridge if you can get a compatible one for much less? In general, brand name cartridges are reliable and safe. If money is not a concern and you absolutely don't want to take any risks, then genuine HP, Dell, Brother, Canon inkjet cartridges are a good choice.
As for photo ink, I recommend you stick with the original company. These inks are a complex blend, and small changes can make a big difference. You want your pictures to last for as long as possible, and that's worth a few extra dollars. So if you have an Epson Stylus printer, buy Epson photo ink cartridges, and get Epson or other high quality photo paper.
To save money on genuine printer ink, consider buying online. You can compare prices and get significant discounts over buying at a local store. Plus, it's extremely convenient, saves gas, and shipping is usually fast.
One caution: be wary of very cheap brand name cartridges. Unfortunately, counterfeit ink cartridges are becoming more and more common. Many of these are produced overseas in third-world countries where laws and regulations are weak. Dirt cheap ink is often of low quality, causes many problems and headaches, and can even damage your printer. I was once a fan of cheap ink, until one cartridge ruined my Epson printer. Remember, bad ink can ruin a good printer.
My advice is to avoid ultra cheap ink and imported cartridges, especially from no-name sellers. If it seems too good to be true, it's probably a fake. To be safe, buy your HP, Lexmark, and other brand name inks from a reliable inkjet supply company.