Number of Santas = (Number of Households * Calories consumed at each household)
----------------------------------------------------------
Number of Calories a Santa needs
Google searching for "Calories in a mince pie" yields 289, Sweet Sherry gives 68, and a half glass of skim milk is around 60 Calories. We can leave out carrots for the Reindeer because Santa won't be eating those. Not all households will approve of - or be able to afford - alcohol, but we assume that all relevant households will offer something to Santa if they can, which is where the small glass of milk comes in; that gives a range 60 - 400 Calories which Santa is known to consume per household. Most of the world is poorer than the USA, but most people are kind, so err on the lower side but not right at the low end. Say 150 Calories consumed per household visit.
The WikiPedia page "List of countries by number of households" sums to 1,587,890,386. Not all households have children, and this perfectly servicable blog post suggests that 20% of adults in the USA live alone (20% of household); 8% live with only a partner (each partner counted halves that number to 4% of households), round that to 25% and then handwave it to 15% globally because childbirth and population growth declines with the wealth of a country and globally it will be more households with children than the USA. Knock 15% off the household count Santa needs to visit, for "no children" as an estimate. 1.348 Billion.
And not all children are good - but Stephen Pinker and Hans Rosling have both argued that the world is a better place than media presents, including living conditions, treatment of children, and education. It seems that should translate to fewer life stressors, more coping strategies, and therefore better behaved children than in the past, so that won't change the number of households Santa visits in a significant way compared to the low precision of the estimate of childfree households, so no change to the numbers here.
Without wishing to get too personal, Santa is a generously proportioned fellow - 300lbs if he's an ounce. But he neither turns morbidly obese nor stick thin year after year. And old enough to have a white beard, but not old enough to retire, puts him in his mid 60s, and nobody would dispute that he has a very active job. Assume he is an average height or slightly above and this Calorie Calculator says he should consume ~4,100 Calories per day to maintain weight. He could push that in a day - but not far enough to be ill, and mince pies are quite rich. Say 50% more.
1.348 Billion households * 150 Calories / 6200 Calories in a day = 35 Million Santas
35 Million Santas is almost the population of Canada, and the world population is made up of almost 0.5% Santa.
This may seem a surprisingly large number, but it is not far from agreement with @user3067860 who calculated 300,000 for the USA alone based on the postal service. We have a number 100x more than that, but there are almost 200x more countries than USA - many with less dense population centers and less well developed postal routes and more households.
@takintoolong calculates 13 Million based on number of households, but assumes delivery can take 24 hours and @KerrAvon2055 comments a doubling or tripling of the numbers, which brings it into the same ballpark.
It could be, of course, that the concept of "one Santa" and "multiple Santas" doesn't apply in the same way as to the rest of us. One Santa, multiple bodies. Many models for such an organism have been speculated about - technologically such as The Borg Hivemind or Peter F. Hamilton's "Multiple Person", biologically in reality with the mycorrhizal connections of "one fungus" underground, or theologically with the Christian Holy Trinity of one Deity and three instantiations. Perhaps Santa requires a new proposal of this kind?
But, at least on Christmas Eve night, there are enough Santas to sink a battleship.
