The age of the universe is a tough thing to define and measure. Often in astronomy we’ll use a unit of time called the Hubble Time, which is the inverse of the Hubble parameter. For H[sub]0[/sub] = 70 km/s/Mpc, the Hubble Time H[sub]0[/sub][sup]-1[/sup] is about 14 billion years. The Hubble Time is by design close to the age of the Universe, but it could actually be greater or smaller.
No, that’s the Planck time. By contrast, there appear to be a number of different definitions of a “jiffy”, all far, far longer than this. Tolman’s definition - the time it takes for light to cross a nucleon - is the one I’ve come across before, though I’ve never heard a particle or nuclear physicist actually use the term in practise. That said, knowing that the time required is about 10[sup]-24[/sup] seconds is useful if you’re studying them (nucleons that is, not physicists) and the number is relevant in the unfolding of the early stages of the Big Bang.
whoops 
If an aeon is a billion years, I make that to be 3.15 x 10[sup]13[/sup] seconds, or 3.15 x 10[sup]22[/sup] nanoseconds. But I might have misplaced a decimal point somewhere along the line…
I make it 3.16 x 10[sup]16[/sup] seconds.
The age of the universe might be the longest time that makes sense to talk about, but it is not a unit of time, per the OP.
alterego, infinity is not a unit. It does not quantify time. As the definition says, it represents the concept of a boundless quantity. You couldn’t say, “Honey, I’m running out to the edge of the universe, I’ll be back in 2 infinities, maybe 3 if traffic is bad.”
chappachula, I have never heard of this definition of a jiffy. Computer scientists use a jiffy to mean 0.01 sec., probably because it slips off the tongue more easily than centisecond.
Hmm Q.E.S, let’s see:
60 seconds in one minute
x 60 minutes in one hour = 3600
x 24 hours in one day = 86,4000
x 365 days in one year = 31,536,000 or 3.15 x 10[sup]7[/sup] seconds in one year.
Ah yes, I multiplied by a million, not a billion. As you were.
Longest = The time it takes the person in front of you at a toll booth to search there seats for a dime.
Shortest = The time between the light turning green and the cab driver behind you honking to get you moving.