I think the answer to the above question is ten years from the date of commercial release of the printer (see http://support.hp.com/us-en/retired-products, "HP stops supporting most products after 10 years.")
A printer is worthless without a steady supply of ink. Two of the ink cartridges HP recommends for my HP Photosmart 8750 have been discontinued. These are the 101 and 102 cartridges, necessary for the "9-ink system" HP advertises (see http://h10010.www1.hp.com/wwpc/pscmisc/vac/us/product_pdfs/426170.pdf). Cartridges are still available, for the moment, for an "8-ink system", but the quality of the prints in my hands does not equal that of the "9-ink system".
The copyright on the "HP Photosmart 8700 series User's Guide" is 2005 (presumably reflecting the year of release of the printer), and I bought mine in 11/07. So it would appear that my printer was supported for about seven or eight years. This interval is unacceptably short for me, and the printer I buy as a replacement will not be from HP.
Perhaps reveiws of printers should include information on how long manufacturers will commit to supplying ink for the printers.