I would use a modeler that uses solids, like Vellum Cobalt or SolidWorks (both on the list). However, those aren't free or even low-cost. However, they make creating objects like coffee cups a lot easier and they're a lot more precise.
Edit: The post was removed, but the question was: which program to use to design coffee cups with for ordering with Shapeways.
Sorry about nuking the post, we had a race condition :) I realized that all product names on that list [1] were clickable, and so I decided to first look at the products one by one and then come back with more specific questions.
Would Sketch Up work in your opinion? Also Mathematica is available under non-commercial license for $295, which is reasonable (and I always wanted a copy of it anyways).
I'd advise you not to use SketchUp for this. When creating organic shapes it's best to use solids [1], not mesh modeling. Otherwise your coffee cups will look like they've escaped from Tron.
Ashlar has a lite version of Cobalt, called Argon - a commercial license costs $1200 or you can rent it [2]. There's also an educational license for $200 [3].
A less costly program that supports solids is TurboCAD, at $500 [4]. I've never used it, but like Ashlar Vellum, they've been around forever.
Sketch Up would not be a good option because it produces mesh models which look like garbage when printed, a good low cost Nurbs modeling software that produces true curves for digital fabrication would be Rhino 3d. The educational version of Rhino is $195. http://www.rhino3d.com/
Edit: and if you want to make your cups parametric like the examples the grasshopper plugin for Rhino is the way to go http://www.grasshopper3d.com/
They're targeting hobbyists (software is completely free) that want a sketchup-like environment. They even provide a 3d printing service for you to upload STL files to.
That actually looks promising. To my knowledge, it's the first gratis solid modeler. The user interface is very similar to Autodesk's Inventor Fusion. It's also on the Shapeways' list of supported programs (by way of STL -- I find it odd that they don't use ACIS, but hey.)
Edit: The post was removed, but the question was: which program to use to design coffee cups with for ordering with Shapeways.