A distribution function, a pdf, has the property that its values are >= 0 and the integral of the pdf over -inf to +inf must be 1. But the integrand, that is the pdf, can take any value >= 0, including values greater than 1.
In other words, there is no reason, a priori, to believe that a pdf value > 1 indicates a problem.
You can think about this for the normal curve by considering what reducing the variance means. Smaller variance values concentrate the probability mass in the centre. Given that the total mass is always one, as the mass concentrates in the centre, the peak value must increase. You can see that trend in the graph the you link to.
What you should do is compare the output of your code with known good implementations. For instance, Wolfram Alpha gives the same value as you quote: http://www.wolframalpha.com/input/?i=normal+distribution+pdf+mean%3D0+standard+deviation%3D0.1+x%3D0&x=6&y=7
Do a little more testing of this nature, captured in a unit test, and you will be able to rely on your code with confidence.