This thread is for everyone so inclined to share their experiences in printing photos on the cheap. I'll start.
Speaking for myself, I like to print my photos and post on a wall at home to see if they work. This means I print a lot of A4/A3 size prints that will never see any distribution. Thus my wish to make reasonably good draft quality prints dirt cheap.
My Epson 3800 is not bad, but its ink really requires some kind of photo paper. Plain paper just soaks up the ink, all other papers impact budget significantly.
The ink I have found to be surprisingly good is Epson's Durabrite. It's a CMYK pigment ink with a resin coating that helps it stay on the surface of plain paper, and stick reasonably well to glossy paper. It's water-based but once dry it's rather waterproof.
Epson uses Durabrite in many non-photo printers like the Workforce series. Most of those printers use tiny consumer-grade cartridges that drive up ink cost to ridiculous levels, but the Workforce Pro series is an exception with cartridges in the 50-100 ml range. The output on plain paper cannot compare to what the 3800 does on Presentation Matte, but it's definitely got the "wow, is this plain paper?" effect. Resolution is lower, smallest drops larger, and with only CMYK dot patterns become obvious at a close look. So you want to print big.
But printing big on a shoestring means finding the cheapest ink as well as paper. There are some third party inks, including one set sold by Jon Cone to closely match Epson's ink. And you need either refillable cartridges or a CIS system.
Letter/A4 size paper:
The best cheap plain paper I have found on the US market for Durabrite and similar pigment ink is HP Bright White Inkjet Paper (HPB1124). There is good black density and saturation, and less bleed-through than on all other plain papers I tried. Can usually be found around $10/ream - I got a big supply from Sam's Club for $7/ream last year.
Epson's own inkjet paper is unimpressive in comparison, at least as of 2014. Sometimes suppliers or formulations change.
Hammermill Color Laser Gloss: This paper is not intended for inks, but was a very interesting experiment. Being a glossy paper (similar in feel to what you find in some magazines with a glossy sheen to the pages), color gamut really pops. Until you get into denser shadows. the paper holds far less ink than a matte paper, and the print driver needs to be tweaked to accommodate for that, down to -30-40% on the ink density slider. Once you get everything tweaked, output is close to magazine quality. I use it for a presentation portfolio, and also for text output like resume and other presentation material. This paper is extremely sensitive to fingerprints (affects how ink settles in dense areas) so handle it carefully.
A3/13x19 paper: I have tried two papers:
Mohawk color copy premium 105 gsm 13x19" (11-116): this paper prints reasonably well with Durabrite. Surface is smoother and probably less porous than most plain paper, which affects color balance slightly. Not a big problem with color draft prints, but a custom profile could help a little. Retains detail well with no visible smear or puddling (is that a word?). Choosing Premium Presentation Matte Paper in the driver gives dense and detailed prints but increases the need for a custom profile.
Hammermill Tidal MP 11x17": This was a waste of time and money, not as compatible with Durabrite inks. Output gets a strange sheen, paper soaks some inks more than others I think.
Now, about the actual printers that I have tried.
Epson WP-4020: Letter-size workhorse. Large tanks, fast output, impressive output for photos for a few pennies per full page on the Hammermill glossy if you have the patience to get it right.
Epson WF-7520: 13x19" printer, same great print quality as 4020 but unfortunately tiny cartridges that not only drive up ink cost but also increase probability of getting a 13x19 photo print interrupted by an empty cartridge to around 10-25% chance for each page. A continuous ink system might help if it has a manual reset button for the chips so you can reset before each print job. Auto reset refillable cartridges will still interrupt when they tell the printer that they are empty.
Epson WF-7620: New "PrecisionCore" printheads, perhaps slightly better resolution due to more variable droplet sizes, slightly faster than 7520, otherwise very similar.
Others to consider:
4530/4540 - previous gen, same as 4020 + all in once.
4630-4640: Current gen letter size "PrecisionCore" workhorses but 4 chips instead of 2 chips on 76xx/36xx series, so twice as fast.
I am now getting a refurbished 4533 from Epson, this is a enterprise version of the 4530 with 3 years warranty and presumably larger duty cycle whatever that means.