Do the dead outnumber the living?, by Wesley Stephenson. From the BBC via getstats.
Answer: yes, by a factor of about 15 to 1. 108 billion or so people have been born since 50,000 BC; 7 billion are alive today.
This is one of those questions that I’m surprised to even see asked. The BBC article is based on estimates from the Population Reference Bureau; if you trace them back you find they come from an article called How many people have ever lived on earth?, by Carl Haub, the PRB’s chief demographer. As far as I can tell the estimate just comes from simple arithmetic on historical estimates of populations and birth rates. The estimate goes by taking the birth rate times the population for each year from 50,000 BC to the present, and adding those up. That is, however, a lot of arithmetic and requires a lot of guesswork.
Is there some quick way to see that there have been at least fourteen billion human births since the beginning of time, and therefore there are more people dead than alive?
God plays dice 
I think things universally require educated guesses, since before around the 19th century there aren’t consistent birth, death, or population records. However, using some fairly conservative educated guesses, I think we can do it.
We can assume the population of the world averaged at least 100 million from 1 AD to 1000 AD and 300 million since 1000 AD. http://en.wikipedia.org/wiki/World_population_estimates seems to indicate experts would agree on those bounds.
As can also assume that a generation, for population purposes, is less than 50 years, e.g. every 50 years there are at least 300 million births between 1000 and 1900. Given that US life expectancy at birth in 1900 (the end of our study, and thus probably close to the maximum value over the entire period) was 46.3 (male) or 48.3 (female) years, that seems reasonable.
That means that in each of the 18 50-year periods between 1000 and 1900 we had at least 300 million births, giving 5.4 billion total, and in each of the 20 50-year periods between 1 and 1000 we had at least 100 million births, giving another 2 billion total, so we’ve found a lower bound of 7.4 billion births between 1 and 1900. Given that it is certain than less than 400 million people alive in 1900 are alive today, we’ve found more than 7 billion people who lived before today.
An interesting follow up: assuming that the birth rates are increasing, will there ever be a time (theoretically) when the number of living is exactly the same as the number of people who have died before that point?