Anybody can make, and have approved, a minimum equipment list (MEL). Few do this without first going to a Master Minimum Equipment List (MMEL) maintained by the FAA (with respect to N registered equipment). A MEL can be developed with or without an existing MMEL...but generally operators are loathe to do so because of the work involved, and because of liability concerns. The MMEL represents preapproved material; drawing from this material short cuts the process considerably.
Most light airplanes have no MMEL. It's important to understand that MMEL or not, a MEL is aircraft specific; it's approved for a specific aircraft, or specific aircrafts. It's not issued for all Cessna 310's, for example...but for NXXXXX...the specific registration and serial number, and is applicable to just that airplane (or a fleet or airplanes attached to that particular MEL, where applicable).
When the MEL is in use, it plays the same role as a supplemental type certificate, modifing the condition of the aircraft in an approved manner.