Difference between Needn´t and Don´t need to.

1. We knew it wasn't necessary so we didn't do it.
We didn't need to have any vaccinations when we went to Morocco.
Here only didn't need to is possible.

2. We knew it wasn't necessary but we did it anyway. Here both are possible and there's no difference in meaning.

a) We didn't need to go to the meeting, but we knew John would be there and we wanted to see him, so we went anyway.
b) We needn't have gone to the meeting but we knew John would be there and we wanted to see him, so we went anyway.

3. We didn't know it wasn't necessary so we did it and found out later. Again both are possible.

a) What an idiot I was! I spent the whole weekend studying and I didn't need to at all - the exam's next month, not this month!
b) What an idiot I was! I spent the whole weekend studying and I needn't have done it at all - the exam's next month, not this month!

So - needn't have always means that the event happened, whether we knew about it in advance or not. Some examples I got by Googling it were :
he needn't have died, she needn't have worried, you needn't have bothered - in all cases it happened but wasn't necessary.

didn't need to on the other hand may mean either it happened or not. Again examples from Google include : 
I didn't need to see that! and The things they carried and didn't need to. - ie it happened
Solved all my gift problems and didn't need to traipse through loads of shops - ie it didn't happen