Does this intersection algorithm work like it's supposed to?
Since there's no answer yet, I'll take a crack at it.

My first impression is that the nesting is somewhat deep and some of the variables could be moved closer to its site of usage. Here's one possible refactor:

float BoundingSphere::Intersects(Ray ray)
{
    D3DXVECTOR3 cToO = ray.Origin() - centre;
    float rSquared = radius * radius;
    if(D3DXVec3Dot(&amp;cToO, &amp;cToO) &lt;= rSquared) return 0;

    D3DXVECTOR3 direction = ray.Direction();
    if(D3DXVec3Dot(&amp;cToO, &amp;direction) &gt; 0) return -1;

    D3DXVECTOR3 vec = cToO - direction * D3DXVec3Dot(&amp;cToO, &amp;direction);
    float vSquared = D3DXVec3Dot(&amp;vec, &amp;vec);
    if(vSquared &gt; rSquared) return -1;
    // ...
}


There should be someway to multiple a D3DXVECTOR3 with a scalar value at once. Even if that's not directly supported it's trivial to overload the operator *= yourself. The return is also getting rather long. I broken that long statement into more digestible pieces:

    float mul = sqrt(rSquared - vSquared);
    D3DXVECTOR3 normDir = *D3DXVec3Normalize(&amp;direction, &amp;direction);
    normDir *= mul;

    return D3DXVec3Length(&amp;(ray.Origin() - centre - vec + normDir));
}


I haven't looked at the collision in too much detail, it seems ok from a glance.


  it should return -1 if there is no collision, 0 if the origin of the ray is inside the sphere...


It sounds like you have a clear idea of how this method is suppose to behave. Why not grab a unit testing framework, like google test, and write a unit test for each of those cases? Testing BoundingSphere::Intersects can be as simple as this:

TEST(BoundingSphereTest, testRayInsideSphere)
{
    BoundingSphere testSphere(D3DXVECTOR3(0, 0, 0), 42);
    Ray testRay(0, 0);

    EXPECT_EQ(-1, testSphere.Intersects(testRay));
}


Note, I'm just guessing on how those objects are constructed but this should give you the main idea. Fix them up as appropriate.