Well, Toyota has a very good fame in several different countries across the globe, that is for sure.
The japanese brand bets on durability and quality to attract customers. Of course not all of their cars are so famous, but models such as the Corolla, are true "classics". Many people prefer to have a car that will not break as often. Japanese cars usually use CVT tranmissions on their cars (so does the brand Honda), and this transmission for automatic cars is way more reliable as well.
Toyota cars are the option where the person gets the "best" for less...so that is why I believe they get their fame from.