The land mammal with the most teeth is the South American giant armadillo, with 74.
Sharks have the most teeth of any vertebrates during their lifetime, because their teeth are anchored into flesh alone and are continuously replaced. The requiem shark is estimated to grow as many as 30,000 teeth during an average full lifespan. The great white shark is estimated to only generate on the order of 10,000 per lifetime.
If you count their chitinous scraping radula as a 'tooth', the record-holder among all known animals is the umbrella slug (a sea slug), which is estimated to generate as many as 750,000 of these chitinous 'teeth' during a full life.