As many or as few as you’d like.
Generally, we recommend that prizes be given to at least the top 3 players or teams.  After that, we have lots of options.  We can give prizes to each round winner.  Prizes can be randomly awarded to players via the “Wheel of Fun”.  We can find a way to give away as many prizes as you can come up with.
Total side note:
We did an event for a company this past Christmas season where they had tables and tables of really great prizes for their employees to choose from.  The table that won trivia had their first pick of prizes.  Second place table went next.  Etc.  It was really fun to watch and made for a real competitive trivia game!