This one confused the hell out of all of us, me included, until I looked it up. Here’s the answer:

Needn’t and don’t need to

There is also a difference in use when these verbs are used to describe present situations. We can use both needn’t and don’t need to to give permission to someone not to do something in the immediate future. We can also use need as a noun here:

However, when we are talking about general necessity, we normally use don’t need to:

Needn’t have and didn’t need to

There are actually three possibilities :

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. E.g.:
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 that it happened or not. E.g. :
I didn’t need to see that! and The things they carried and didn’t need to. – i.e. it happened
Solved all my gift problems and didn’t need to traipse through loads of shops – ie it didn’t happen

Resource: http://www.eslhq.com/forums/esl-forums/english-questions/neednt-dont-need-6788/

Need

Note from the above examples that need can either act as a modal verb or as an ordinary verb. When it acts as a modal auxiliary verb it is nearly always used in negative sentences, as the above examples illustrate, although it is sometimes also used in questions as a modal verb:

When it is used as an ordinary verb with to before the following infinitive and with an s in the third person singular, it appears in both affirmative and negative sentences and in questions:

Resource: http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv317.shtml