Haemoglobin

 

This is an image of a haemoglobin molecule using a ribbon diagram. 

Haemoglobin molecules have four subunits, normally these are two 'alpha' amino acid chains and two 'beta' amino acid chains - labeled as ∝₁, ∝₂, ꞵ₁, ꞵ₂.

Each subunit contains a haem group (the balls and sticks you can see in the diagram above). An oxygen molecule can reversibly bind to the haem group. So one haemoglobin molecule can bind four oxygen molecules, and no more.

A key point here is that it's not a rigid, immovable structure, and you can see it flexing between two conformations (more on this later).

Image by BerserkerBen and used unmodified from Wikipedia under licence https://creativecommons.org/licenses/by-sa/3.0/