I've got two hard questions that I need help with...
1. Cytochromes do not bind oxygen, regardless of whether the iron is present as +2 or +3. Why then can haemoglobin carry oxygen when the iron is +2?

AND

2.Why can't haemoglobin bind oxygen when the iron is +3?

1. Actually, some cytochromes apparently do bind oxygen:

Crystal Structures of an Oxygen-binding Cytochrome c from Rhodobacter sphaeroides -- Leys et al. 275 (21): 16050 -- Journal of Biological Chemistry

Check out these papers:

Hemoglobin Transports Oxygen Efficiently by Binding Oxygen Cooperatively

2. Iron (III) undoubtedly doesn't have the same electron affinity as iron (II). As a result, it's likely that oxygen would be bound irreversibly.

OK thanks, but my main question was "Why then can haemoglobin carry oxygen when the iron is +2?"

That's sort of like asking why do we die? We just do -- so it goes with haemoglobin.

It really has to do with the overall electron affinity of the iron -- and you need to compare it to other oxidation states of iron to understand why. It has less electron affinity when in the +2 oxidation state than when in the +3 oxidation state. Oxygen, of course, is willing to donate electrons. When Iron is in the +3 oxidation state, it wants electrons so badly that it really grabs onto the oxygen and won't let go. When in the +2 oxidation state, it holds on less strongly.

The surrounding protein plays a critical role by donating and absorbing electrons. Its three-dimensional structure changes when oxygen is bound and when it is released. It changes the electron affinity of the Fe+2 so the oxygen can either be bound or release.