Are there any scales other than temperature that have different zero points? For most physical measurements, zero is the same regardless of the units used for the measure:
$0 \mathrm{mi} = 0 \mathrm{km}$
$0 \mathrm{s} = 0 \mathrm{hr}$
but for absolute temperatures, different systems have different zeros:
$0 ^\circ\mathrm{C} \neq 0\,\mathrm{K}$
Are there any other physical, measurable quantities (other than temperature) that have different zero points?
I'm looking for measurable quantities that are applicable anywhere -- things like voltage or temperature, not local quantities like "distance from the Empire State Building".
 A: Motion.
Velocity is obviously relative, and no "absolute rest" frame is known to exist.
Even acceleration, which is in a sense absolute, is sometimes specified relative to a local inertial frame (ie. freefall), sometimes relative to the distant stars (so you can talk about the acceleration of astronomical bodies due to gravity), and most commonly in everyday life, relative to the Earth. You think you are sitting still at your desk, but relative to a local inertial frame you are actually being accelerated upwards at about $9.8 m/s^2$ due to the pressure of the chair on your ass!
A: Gauge pressure.
From Wikipedia:

Gauge pressure is zero-referenced against ambient air pressure, so it is equal to absolute pressure minus atmospheric pressure.

A: Time, in which case each system's zero point is often called its epoch:
http://en.wikipedia.org/wiki/Epoch_%28reference_date%29
A: Sound can be measured in deciBels ($\mathrm{dB}$) but also as an intensity measured in $\mathrm{W/m^2}$. 
$0\,\mathrm{dB}$ on this scale is equal to $1\times10^{-12}\,\mathrm{W/m^2}$.
A: Gravitational potential energy (in a constant gravitational field such as near the Earth).  This is the usual scenario in elementary questions for high-school students.  One may use the starting point of a body as zero or the end point or the ground.
A: The scale used to define positions on a highway depends on the point chosen for the Zero Marker.  There is a difference between defining a position on a highway, like Mile #25 or Exit 125, and a distance on that highway: it's 30 km from Km 15 to Km 45.
The same thing is true in temperature scales, where we need to distinguish between labelling a position ("the freezing point of water") and measuring a temperature difference ("the freezer was 38 Celsius degrees cooler than the room")
I once read a news report saying, "February's average high of -6 degrees Celsius was twice as cold as the historical average of -3 degrees Celsius..."
A: One that has many zero points is the standard Gibbs free energy of formation:
each element has their own zero point.
A: Luminosity.
The Magnitude of a star is a logarithmic scale with an arbitrary zero point.
The SI unit of brightness is the Candela or or there is luminosity if direction is not accounted for.
From Wikipedia: 

In SI units luminosity is measured in joules per second or watts.
  Values for luminosity are often given in the terms of the luminosity
  of the Sun, which has a total power output of 3.846×1026 W.[2] The
  symbol for solar luminosity is L⊙. Luminosity can also be given in
  terms of magnitude. The absolute bolometric magnitude (Mbol) of an
  object is a logarithmic measure of its total energy emission.

A: Another example of an arbitrarily selected zero point is longitude. This was not always measured from the Greenwich meridian - Paris has been used, and the ancient Greeks (Ptolemy, specifically) used an island believed to exist off the west coast of Africa* in order to avoid dealing with negative numbers.

Really, though, none of the examples anyone have mentioned do what temperature does in terms of having a natural zero point which is not universally used. All of these examples (as of this posting) are either logarithmic scales (and all have a true zero point at negative infinity), are measuring position rather than quantity.
And you can't do this for time because of relativity - there's no reasonable point of reference for the International Terrestrial Reference Frame (i.e. the time kept by an ideal clock on Earth's surface at sea level) at the beginning of the universe, so we can't measure from the big bang even if we could otherwise determine the "age of the universe" down to the nanosecond.
Temperature has an arbitrary zero point because people have been measuring temperature since before the fact that there is an absolute zero was discovered.
*Of course there are such islands, but it's not known which he used and none correlate precisely to his maps.
A: Height / altitude. From Wikipedia:

  
*
  
*Indicated altitude – the altimeter reading
  
*Absolute altitude – altitude in terms of the distance above the ground directly below
  
*True altitude – altitude in terms of elevation above sea level
  
*Height – altitude in terms of the distance above a certain point
  
*Pressure altitude – the air pressure in terms of altitude in the International Standard Atmosphere
  
*Density altitude – the density of the air in terms of altitude in the International Standard Atmosphere
  

I suppose you could define an "absolute altitude" as distance from the center of the Earth.
