How many people live on less than $1/day?

It's weird how hard this question is to answer. The two kinds of statistics I'm aware of are household surveys, which ask people to estimate their consumption, and national account statistics, like per capita GDP, which measure output. Both are seriously flawed and different methods give dramatically different answers. For example, Sala-i-Martin's 2002 paper The World Distribution of Income (estimated from Individual Country Distributions) argues that the number of poor has dropped dramatically from 1976-1998, while Ravallion and Chen's paper How have the world’s poorest fared in the 1980s? says that poverty rates have been close to flat from 1987-1998; and the differences aren't explained by the differnet time periods they look at. Some of the controversy is addressed in Ravallion's response to Sala-i-Martin.

A summary of the household survey vs. national accounts statistics dilemma is in the abstract of Deaton's 2005 paper Measuring Poverty in a Growing World (or measuring growth in a poor world):

Abstract—The extent to which growth reduces global poverty has been disputed for 30 years. Although there are better data than ever before, controversies are not resolved. A major problem is that consumption measured from household surveys, which is used to measure poverty, grows less rapidly than consumption measured in national accounts, in the world as a whole and in large countries, particularly India, China, and the United States. In consequence, measured poverty has fallen less rapidly than appears warranted by measured growth in poor countries. One plausible cause is that richer households are less likely to participate in surveys. But growth in the national accounts is also upward biased, and consumption in the national accounts contains large and rapidly growing items that are not consumed by the poor and not included in surveys. So it is possible for consumption of the poor to grow less rapidly than national consumption, without any increase in measured inequality. Current statistical procedures in poor countries understate the rate of global poverty reduction, and overstate growth in the world.

Another pitfall is how people approach the topic with preconceptions (also known as null hypotheses). For example, the paper by two World Bank economists [Dollar, David and Aart Kraay (2002) “Growth is Good for the Poor,” Journal of Economic Growth, 7(3) 195-225.] should really be titled "Growth cannot be shown to not be good for the poor," since rather than showing that the bottom 20% receive an equal share of growth, they fail to reject the null hypothesis that the bottom 20% receive an equal share of growth.

Got it? They find that a 1% increase in GDP increase the income of the bottom 20% by an amount that is not significantly different from 1%. But that doesn't mean it's close to 1%, just that their data is sufficiently noisy that 1% lies within their error bars. So maybe "Growth might be good for the poor" would be a better way to put it.

Also, household surveys are probably more accurate for levels of consumption by the poor than for the relative share of consumption of the poor (since the rich underreport consumption or don't reply to surveys). But this paper uses household surveys only to establish the poor's share of consumption, and then estimates the level of consumption by multiplying this by GDP. Since GDP in India (for example) has grown 5-10%/decade faster than consumption measured by surveys, this should systematically overestimate both the level of income the poor get, and the rate at which it grows.