Sven

@Yan:
The problem here is just that your face normals are inconsistent. Only the bottom triangle (3rd face) is pointed IN, while the other 3 triangles are pointed OUT. If you replace:
face = [1,2,3;3,2,4;1,2,4;1,3,4];
with
face = [1,2,3;3,2,4;2,1,4;1,3,4];

and use (...,'flipnormals',true), then your input will work just fine.

@CUP:
It's actually a 3D picture, it's just that by default it has no shading and is looking from the XY direction. Try this:
pts = rand(10,3) * 10 ;
growbubbles(pts)
view(3), axis image, camlight

@JD:
The issue is that your input is "gridded data" not "triangulated data" because each of x, y, z is a 20-by-20 matrix, rather than a set of vertices and triangles.
This can be handled by stlwrite (see the help file for the "triangulation" parameter), but you'll need to understand that the default "triangulation" of gridded data is a delaunayTri of the X-Y 2D data. In this sense you have repeated X-Y pairs (one at the top of the sphere, one at the bottom). The warning you're getting comes from "delaunay", not from "stlwrite".
You can overcome this by specifying how you want your gridded data triangulated:

stlwrite('test1.stl',x,y,z,'mode','ascii','triangulation','f')

Note that you'll need "mesh2tri" from http://www.mathworks.com/matlabcentral/fileexchange/28327 for this to work. I will ask Kevin for permission to include it in stlwrite (it's a small but very handy function) for a next release.

Is there a way to find the coordinates of face normals that are pointed in different directions? Majority of my faces are pointed in the right direction but a few are in the opposite direction. I can use 'flipnormals' but that flips every face, not just the few I need flipped. Any help is appreciated.

@Yan:
The problem here is just that your face normals are inconsistent. Only the bottom triangle (3rd face) is pointed IN, while the other 3 triangles are pointed OUT. If you replace:
face = [1,2,3;3,2,4;1,2,4;1,3,4];
with
face = [1,2,3;3,2,4;2,1,4;1,3,4];

and use (...,'flipnormals',true), then your input will work just fine.