We are quite capable of running our own country, thank you. History shows that not having a King or Queen does not make things always a lot better when it comes to the man being in charge....
The King/Queen is mostly (although not entirely) a ceremonial role in our country. The "not entirely" part I actually like. I hope it will prevent some nut-cracker taking over in one point of time. Of course we have been lucky to have some pretty intelligent royal family so far...which is not always the case. However, the democracy and the king/queen form a nice balance in that way IMHO.
If the majority of people would have wanted a republic in The Netherlands, there would be one already. However, we were lucky to have a very capable queen the past 33 years, who is first of all a great representative for our country, opening doors for businesses and organizations around the world which is good for our economy (we are one of the last three AAA-rated countries in Europe.....).
Apart from that, she has a very important role for the people of the Dutch kingdom when it comes to f.i. national tragedies happening. IMHO those two functions alone are done better by a queen/king than any president who is only a temporary figure (I REALLY have no clue who the president of Germany is at the moment...f.i.) for a couple of years.
Apart from that, we wouldn't have a Queen's/King's day, one of the very few national celebrations over here, one that almost everyone enjoys.