Does it exist a free interactive geometry software, like GeoGebra, which works for 3D geometry? I would be able to draw spheres, great circles, and so on.
GeoGebra 5.0 (with 3D) has been released:
There will be a public preview of GeoGebra 3D soon. Keep an eye on the GeoGebra forums :)
Geomview is fairly flexible, and allows you to work in Euclidean, spherical or hyperbolic geometry. Depending on which operating system you use it might be easier or harder to get it installed. It made it into the Ubuntu repositories recently, so if you're running Ubuntu it takes little effort to install.
That said, it's not the easiest software to use -- quite a ways away from the interface of GeoGebra. More often than not, if I need a high-quality rendered image of something 3-dimensional, I code a PovRay script and render it.
Blender is open-source and interactive. It appears to be quite flexible -- it's used to produce models for 3d video games, for example. I haven't really got comfortable using it, though.
You can try pgftikz http://www.texample.net/tikz/examples/
here is a complete list of softwares:
I would be able to draw spheres, great circles, and so on.
You can easily draw:
cube, cuboid, cylinder, line, line segment, plane, point, polygon, quadrangle (square), sphere, text, triangle, vector.
Rotation is available for: Cuboid, cube, text, cylinder as well.
After you specified some 3d shapes you can also animate their properties by changing the number values. See description on page how to change values: holding down ALT key and using cursor keys. Also have a look at the gallery on the page to see what things you can achieve with this program. It also calculates basic values of the 3d objects.
Currently I am using it a lot to solve vector and plane equations. By the visualization I can check if the result is correct. That is one use case, and it is super helpful for me.
Hope that helps you too.
If you search for a program for 2D drawings, you could use the new Geodrafter 2D.
Update: Geoservant is now available in German, English, Chinese, and Swedish.
Try kd3-surf if you haven't yet found it at http://k3dsurf.sourceforge.net/
Free software and small file size, easy to manipulate.
If you're on a mac, theres a plotting software build in.
Go to Applications / Utilities / Grapher.
It's easy and powerful, can plot 2D and 3D graphs.
Look at the DMelt program. It is free. You can draw 3D functions, parametric functions in 3D. The canvas is called HPlot3D. Look at the at the example galley with math plots.