Do eggs spoil unrefrigerated?

Yes and no. Obviously they'll eventually spoil but eggs are naturally pretty reislent and will usually last two or three weeks unrefridgerated (great news for backpackers!). This is due largely to natural antibactierial qualities in the shell. Temperature, the health of the chicken that laid the egg and the density and state of the shell (ie: cracks) will all effect longevity. A good rule of thumb is if it smells rotten, it is rotten (hence that "rotten egg" smell), otherwise enjoy!