I am looking at possibility of making jewelry using CAD-CAM. And I wander if BobCAD is something I can use to make designs that I need. It's mainly non geometrical shapes. More like free hand art. You can see the examples of what we make here: http://www.enamelartjewelry.com/. It's to make wax models on CNC mill for investment casting.

Also do I need 3 or 4 axis machine to make something like this?

BobCAD is capable but you might want to look at Rhino for CAD and Visual Mill 6.0 Pro for CAM. Free form shapes such as these are Rhino's specialty. 4 and 5 Axis Machining is Mastercam's specialty.

If you have a nice budget you might also look into Solidworks 2008 and Mastercam X2.

It really depends on your budget, but ultimately what you feel comfortable with.

Where one person is comfortable BObCAD another maybe more comfortable with Pro/E Wild Fire.

IMHO I prefer Alibre V10 Professional for 98% CAD.

It is up to you, and make sure what ever you choose is right for what you need.

BobCAD is capable but you might want to look at Rhino for CAD and Visual Mill 6.0 Pro for CAM
Does it mean that BobCAD is not suitable for such application? Or not recommended? Or it's just too difficult to do free form designs using it?

The human interface on packages vary greatly.
Try some demos, and you will soon see what you DON'T like, then ask about what's left to try. You really need free form CAD modeling, with some CAM program that is bearable to use. You shouldn't have to draw (CAD) with a CAM package, and you shouldn't have to CAM with a CAD package.
IMHO, put the two together and you get something thats a b*#jch to learn.
Designing something in 3D and machining it are very different things. You can rotate it while you are designing it, but have much more restriction moving it while machining it. Concepts are different. We add stuff to a 3D model, and remove stuff with a CAM package... I like drilling holes.
Maybe useful info on this forum:
http://www.3dcadjewelry.com/phpbb/viewtopic.php?f=10&t=902&sid=08b9dfe6f96aad98cd4bdc50b786c49e&p=10691#p10691

Thanks, I understand general ideas. But my question is actually about BobCAD specifically, or its suitability for my intended work.

Problem with BobCAD is that there are no manuals in demo packages. Just some "getting started" PDFs with a couple of very simple examples. So it's hard for the beginner to figure out what it can do. They have a package of training CDs, but you have to buy it. And there are no training materials or any other help on their web site.

When I purchased my machine (SX3 CNC) I was offered a BobCAD license.
I am not bad mouthing it. I just don't like it.
I'm happy I didn't accept the offer. I hate the user interface, the G-code editor that uses non-standard Windows keys, crazy cursor focus, when I hit undo, I thought like most editors it would undo text backwards. It undid ALL my work entered. That's when I said NO MORE, and line renumbering that makes a mess of files. I saved my money. They were even trying to offer me stuff over the phone but could not convince me.
As I said, CAD for CAD and CAM for CAM. Looking at the complex shapes in jewelery, IMHO I think you would be fighting it. Have a look at 3Dcadjewelery.com and ask their opinions. They will soon tell you if it will work OK. end of rant.. My relief valve was stuck open.