The average age of a Pope at their election is 63.5 years old. The average age at the end of their reign is 73.2 years old. That gives an average reign of 9.7 years. The average reign since the very beginning is roughly 7.5 years.
Benedict XVI was 78.0 at his election and his reign will be 7.9 years long.
Young follows Old
There is a distinct pattern of the election of a younger Pope following an older Pope (at election), and vice versa - but their are also exceptions. Here is a chart showing the differences (warning: PDF).
The average difference of the age at election of one Pope compared to the age at election of his predecessor is 10.8 years (median is 11.2).
The biggest differences were -25.0 years (Clement XI following Innocent XII) and +27.0 years (Callistus III following Nicholas V). Benedict XVI was 19.6 years older than John Paul II.
The smallest difference was Clemenet XIII following Benedict XIV - an age difference of only a few weeks (-0.1 years).
Because I know someone will ask, based _purely_ on the averages given above, the closest fit would be Antonio Cardinal Cañizares Llovera who would be 10.6 years younger than Benedict XVI was at his election.
Young follows Old (older only)
Since Benedict XVI was elected at an older age than most, I wanted to look at the same stats, but only including the oldest 10 (Benedict XVI included).
Their average age at election was 77.0 (vs Benedict XVI's 78.0). The low was 72.3 and the high was 79.8 years old.
The average age of their successors was 63.5. The low was 51.3 and the high was 78.3 years old.
That yields a difference, on average, of -13.5 years.
Again, based _purely_ on the averages, the closest fit would be Peter Kodwo Appiah Cardinal Turkson.
Service as a Cardinal
Most Popes have been Cardinals first, although it is not a requirement.
The shortest length of time as a Cardinal before being elected Pope was Nicholas V at 0.3 years. The longest was Benedict XIII at 52.3 years. The average is 14.3 years. (Benedict XVI served as one for 27.8 years.)
Again, purely based on the average above, the next pope might be one of the cardinals that was created in the consistory on 21 Feb 2001. (17 of those created that day will be electors in the conclave.)
Service as Priest and Bishop
Most Popes have been Priests and Bishops first, although it is not a requirement.
The average is 32.6 years as a priest and 19.1 years as a bishop when they are elected Pope.
All of the information above is based on Popes from 1450 to today (and include the anticipated resignation of Pope Benedict XVI on 28 February 2013), unless it explicitly states otherwise.