What are advantages / disadvantages of wiring electric circuits in series and advantages / disadvantages of wiring electric circuits in parallel?

When you wire circuits in series all the electrical loads
(e.g. bulbs) are arranged in a single loop.  There is a single flow of current that goes
through all the loads which cannot be interrupted.  If a single load is interrupted
(e.g. a bulb blows out) everything in the circuit goes out.  If you couldn't tell which
one blew out (a problem with old style Christmas lights) you'd have to check out each
bulb individually until you found one that if replaced allows the whole circuit to light
up again. Each time you add a load the amount of current in each one goes down (e.g.
each bulb gets dimmer).  You can only control the whole set of loads with a switch. 
Compared to a parallel circuit the load on the battery is less so the battery lasts
longer.

In parallel there are several separate current
loops connected to a battery.  When one load goes down it only affects the load in that
loop and leaves the rest unaffected.  Modern Christmas lights are constructed in
parallel so that only one or at most only a few lights go out if one burns out, not the
whole set.  Each loop contributes current going in and out of the battery so that with a
lot of loops this can add up to a lot of current going in and out.  This is a safety
issue.  One, there is part of the circuit with high current. Second, high current means
high heat generated in the wires.  The insulation could melt and cause either a short or
a fire.  (The Mythbusters have a great episode which shows that it is the sparks from a
short and not the temperature of the wires that causes most Christmas tree fires.)  You
can control each loop separately with a switch.  The high current also uses up the
battery faster because because it has to power each loop separately.  Finally, if you
add a loop the rest of loops maintain their current (so the lights don't dim when you
add another bulb).