I'm trying to put an object on the vertices of another object (crosses on a sphere) but I would like all the crosses to be parallel to the sphere's surface, not sticking out.
This is my current setup (using particles):
Blender Stack Exchange is a question and answer site for people who use Blender to create 3D graphics, animations, or games. It only takes a minute to sign up.Sign up to join this community
In the "Rotation" panel of your particle system, choose "Normal" as your "Initial Orientation" (and possibly Phase: 0).
If your crosses are now sideways (this might not be your case), edit your original cross object in Edit mode (Tab) and rotate it so that it lays on its side.
Better explained with pictures:
(P.S. as pointed out in the comments, if you want the particles to stay in place you should set "Physics" to "No")
Edit: in the comment you mention that you would like the "cross" instances to follow the sphere during animation. There are three different approach to this problem, which I'll not explain in detail as they are not the topic for this question: