Is the observable universe equivalent to 'our' light cone? All the objects we can observe (stars, galaxies, ...) must be in our past light cone, since otherwise we couldn't see them. Presumably there are more objects located outside of our observable universe (so far away that we can't see them because it's light can't reach us). 
Is the part of the universe that is visible to us equivalent to 'our' (earth's) past light cone?
 A: They're related, but not exactly the same:


*

*Our past light cone is the part of spacetime from which light has had the time to reach since the Big Bang.

*The observable Universe is the part of space from which light has had the time to reach since the Big Bang. It is bound by the so-called particle horizon.
Note the subtle difference; our past light cone consists of events in spacetime whereas the observable Universe consists of positions in space.
One might think that the distance to the particle horizon is equal to the age of the Universe, times the speed of light, but as PM 2Ring comments, the expansion of the Universe has made the distance much larger (roughly 46.3 billion light-years). However, if you express distances in comoving coordinates — i.e. the coordinates that expand along with the Universe — things become a bit simpler.
In the spacetime diagram below (colored to match Davis 2005), you see our Universe at all times, from $0$ to $\infty$, with time along the $y$ axis and space in comoving coordinates along the $x$ axis. As expansion can be mapped to time, a secondary $y$ axis shows the scale factor $a$, i.e. the size of the Universe relative to today.
Our past light cone is the whole red/orange region extending backward from "here and now" (where the blue lines cross). In contrast, the observable Universe is the thick part of the horizontal blue line. Note the symmetry, highlighting the relation between the two: the length of the blue line equals the width of the "bottom" of the past light cone. Note also that the observable Universe contains regions from which light will never reach if emitted today, namely all region outside the event horizon.

