Is there continuing growth in Christianity around the world or has it stalled/declined? I'm interested in worldwide stats rather than for individual countries.
The numbers appear to be inconclusive, at least according to this site.
It appears the number of Christians is growing, but in terms of percentage of population, some studies show a slight growth, while others show a slight decline. Of course the various studies are over different time periods, so it's impossible, with the given data, to draw any conclusive results.
Wikipedia estimates the 2007 growth rate of Christianity at 1.38%, which appears to be within the range of the various studies cited above.
The answer to this question really depends on how you measure the growth. One way to do so would be to measure the languages to which Christianity is becoming available. Bible translation is probably a lagging indicator, as missionaries often precede the work of translation.
According to Wycliffe Translation Statistics, the number of people win the world who speak languages where no translation work has been either begun or completed is 340 million (slightly more than the population of the United States). This is 5% of the World's population.
So, Christianity is, indeed, continuing to spread across more and more language groups. This is a fulfillment of the prophecies in the book of Revelation that spoke of people from every nation, tribe, and tongue.
I can't find where I saw estimates of when the last language would get a Bible translation, but it's quite feasible to reach that goal in the next hundred years, maybe even 50.
This is directly copied from a Pew Forum Survey under the title "Religious Affiliation":
Compared with their elders today, young people are much less likely to affiliate with any religious tradition or to identify themselves as part of a Christian denomination. Fully one-in-four adults under age 30 (25%) are unaffiliated, describing their religion as "atheist," "agnostic" or "nothing in particular." This compares with less than one-fifth of people in their 30s (19%), 15% of those in their 40s, 14% of those in their 50s and 10% or less among those 60 and older. About two-thirds of young people (68%) say they are members of a Christian denomination and 43% describe themselves as Protestants, compared with 81% of adults ages 30 and older who associate with Christian faiths and 53% who are Protestants.
Based on this information, as well as the other graphs and questions in that survey, I would venture to say that Christianity is not growing, but rather declining. Of course, for every survey that says it's declining, there is probably one that says it's growing...