This is exactly the same outcome as in 2014, although slightly fewer students got the very top grades.
A total of 19.2% passes were A* and A grades - a drop of 0.2%.
Wales failed to close the gap with England but the education minister said the best results had been matched and it was a "strong performance".
But opposition parties said it was a reality check and Wales had come up short.
An improvement in performance in the north east of England (67.2%) saw the region overtake Wales (66.6%) in terms of A* to C grades.
Education Minister Huw Lewis said Wales had "at least matched" its best results.
"This is the result of hard work and sustained effort by both our learners and their teachers and I wholeheartedly congratulate everyone involved on this success," he said.
"I am particularly pleased we have seen such a strong performance at key subjects including English, maths,  Welsh and science."
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There is a difficulty in comparing results for maths, where there has been a further fall in the results of pupils who sat the exam in June.
This year, just 47.5% managed to reach a grade of A*-C, compared with 50.6% last year and 52.8% in 2013.
However, many pupils in Wales sat the exam earlier in the year.
When those results, which tend to be higher, are taken into account, it is expected that figure will rise.
Those results will not be released until the autumn.
Wales still lags behind other parts of the UK, as well as comparable regions of England.
The results show:
GCSE results
Must do better - how did 40 schools challenged to improve perform?
How does it feel for a head teacher as results approach?
Where are we at with GCSE changes?
Northern Irish pupils achieve best results
What is it like to re-take a maths GCSE 22 years later?
The 66.6% score on A*-C puts Wales ahead of just two of the nine regions of England - Yorkshire (65.3%) and the East Midlands (65.9%).
But it lags behind the north east of England (67.2%) and the north west (68.6%).
However, at A*-A grades, Wales scored higher than four of the English regions.
POLITICAL REACTION
Conservative Shadow Education Minister Angela Burns AM said: "Overall results across Wales are - regrettably - still lagging behind England.
"In fact, the attainment gap has widened. That's despite clear promises from Labour's first minister to turn performance around and challenge - and surpass - English results."
Aled Roberts AM, Liberal Democrat education spokesman, called it a "massive reality check" for ministers who had spent months heralding this year as being the one where Wales would see a further narrowing of the gap.
"However much spin the Welsh government issues before results as to why we cannot rely on bare data, the reality of the situation is that they would have been very willing to rely on that same data if it had painted a more positive picture."
Plaid Cymru accused the Welsh government of a "culture of complacency".
Two thirds of Welsh pupils who took GCSEs got A* to C grades, according to this year's results.