Original Equipment Manufacturer (OEM) printer cartridges are products that are manufactured directly by a brand name company, like HP or Canon, and have the manufacturer brand name directly on the product packaging. If you purchase your printer cartridge from a retail web site, OEM or brand name cartridges are typically sold side-by-side with non-brand cartridges, typically called "compatible" or "remanufactured" cartridges, which are typically much less expensive than their brand name counterparts.
The warranty process for OEM cartridges is completely different from compatibles or remanufactured cartridges, which are typically warrantied by the retailer. With OEM printer toner and inkjet cartridges, the warranty is provided directly from the manufacturer. Your retailer will ask you to contact the manufacturer directly if you need to replace a defective OEM cartridge that is still under warranty. The retailer has no choice on this matter, these rules are established by the manufacturers themselves.
Unfortunately, sometimes the manufacturer may be reluctant to provide warranty service on a product that was not purchased directly from them, but this does not change the warranty, and the manufacturer has an obligation to fulfill its warranty regardless of where the product was purchased.
In order to receive warranty service for an OEM product, use the contact phone number listed on the cartridge or on the original product packaging. Have the serial number of your machine ready, if possible, as many manufacturers will ask for it in order to verify the product's warranty. Below is a list of contact information for popular manufacturers, and the typical warranty period for their products.