Before I buy I printer, I check whether compatibles are available for it and also the user reviews of the compatibles. As a few mentioned above, I avoid HP, as while there are compatibles for some of its recent printers, they all have poor user reviews about quality, not working, missing lines, etc.
My last printer was the Canon ip5200 and I’ve used compatibles in it for about 3 years without an issue, even for printing photographs. Unlike my experience with a Lexmark, Epson and HP, I rarely had to do a cleaning cycle when using compatibles. In the end, the printer finally failed. I have replaced it with a Canon ip4950 and am ready to start with compatibles once its originals run out.
One nice thing I also like about Canon is that it does not refuse to print documents just because a colour has ran out. Just press the resume button and it’ll print. The same goes with printing with that colour, useful for using up every last drop of that colour until it fades.