1. Toyota Land Cruiser: The Land Cruiser, in various forms, has been in production since 1951, making it the longest-running nameplate in automotive history. However, there have been significant design changes and updates over the decades, so some might argue that it's not the same "model" throughout its entire lifespan.
2. Volkswagen Beetle: The Beetle, originally known as the Volkswagen Type 1, was produced from 1938 to 2003 (with a brief pause during World War II). It was a single model with relatively minor changes over its long production run. However, some argue that the modern "New Beetle" introduced in 1998 was a new model, thus ending the original Beetle's production in 2003.
Ultimately, the answer depends on how you define the criteria. Both the Land Cruiser and the Beetle have had incredibly long production runs and represent iconic vehicles in automotive history.