Finding neighbors of latitude longitude pair location

Question

I have a list of points (more than a few million) defined by latitude and longitude. I want to find out the neighbors of each point. For example, I want to know for each point, what the nearest point, or what the nearest 4 points? or how many neighbors are within 10km radius?

I want to do it programmatically, please provide some possible solutions.

So far I have used a for loop to find out the nearest neighbor:

//C++ example
for (i=0;i<npoint;i++)
  {
     lat1=latitude[i];
     lon1=longotide[i];
     for(j=0;j<npoint;j++)
        {
            lat2=latitude[j];
            lon2=longotide[j];
            distance = some_function(lat1, lon1, lat2, lon2);
            vDistance.push_back(distance);
         }
      //now we can find the smallest distance from the container
  }

But this only works for a limited data size.