Why do stickers curl? When peeling a sticker off its base, the immediate reaction is that it curls; why is this? I am having trouble finding an answer to this. Could it be that the glued side expands upon contact with the air? And, on a somewhat related note, is this a similar reason for why a ribbon curls when glided over with a blade?
 A: The reason that a sticker curls when it is peeled, is that the force needed to peel it off, stretches the the bottom (the glued side) of the sticker beyond its elastic limit. This causes the bottom to be longer than the top, causing it to curl up.  The same principle applies to a ribbon that is being bent over a sharp edge.   
A: 
*When peeling a sticker off its base, the immediate reaction is that it curls; why is this? 
on a somewhat related note, is this a similar reason for why a ribbon
  curls when glided over with a blade?*

The two phenomena are not different: in the second case you you pull the ribbon across the blunt side of the blade of the scissors (or other tool), and at the same time you press a finger or your palm against the ribbon on the other side, creating a sharp angle of roughly 180° (shaped like a U) around which the ribbon has to bend . This bending takes the fabric beyond its elastic limit and leaves it permanently bent.
In the first case you have the same phenomenon, the glue might some special properties but its role is negligible: usually when you remove a sticker you pull it almost horizontally holding  it with your thumb while sliding your index finger on its surface, and thus making an angle of roughly 170° (allowing for the thickness of your finger). Plastic material is made by polymers and these are deformable only to a certain extent:
synthetic fibres can withstand a certain amount of stretching or bending without being permanently deformed. If the fibres are deformed too much, the polymer molecules cannot be straightened again, so the shape of the fibres is permanently changed.
From wiki:
Plasticity in amorphous materials
Crazing

In amorphous materials, the discussion of “dislocations” is
  inapplicable, since the entire material lacks long range order. These
  materials can still undergo plastic deformation. Since amorphous
  materials, like polymers, are not well-ordered, they contain a large
  amount of free volume, or wasted space. Pulling these materials in
  tension opens up these regions and can give materials a hazy
  appearance. This haziness is the result of crazing, where fibrils are
  formed within the material in regions of high hydrostatic stress. The
  material may go from an ordered appearance to a "crazy" pattern of
  strain and stretch mark

Please note that ribbons for decoration are called curling ribbons

because the are expecially made to curl, or usually poly ribbons as they are made from polymers, like the stickers. Sometimes they are still made of cotton or silk (which is very expensive)
