EDIT Dec 3, 2011: Added Balloon v2 file, with some minor changes to improve slicing with skeinforge. I had the best results when I turned infill off completely. I recommend you review the layers with strings before printing, to make sure the extruder doesn't start/stop in mid-air.
This thing is based on the experiment with strings that I did with Thing8. It is inspired by tc_fea's excellent Fractal Tree 2 ( http://www.thingiverse.com/thing:4340 ). I had shown the printed model of his tree to someone and they asked if it was a balloon. So I thought I'd see what kind of balloon I could make. I am very happy with the end result!
This is a very challenging print. The two times that I've printed the balloon part, a few of the strings failed to make it across the gap. It might take a lot of experimenting to get a perfect print, but it still looks good with a few broken strings.
UPDATE: It turns out it was an issue with the way skeinforge was slicing the STL. I've included a version 2 file below which seems to work better, at least if you turn off infill.
The gondola is printed on its side to create the eight strings that support it hanging from the balloon. It is also oriented at 45 degrees on the build plane so that the topmost wall is more easily bridged, because Skeinforge defaults to 45 degree infill.
Amazingly, those 8 thin strings are enough to support the weight of the balloon, as you can see in the photos.
This was printed on a RapMan 3.0 in black UltiMachine PLA.
This is designed to be printed with 0.3mm layers. If you want to use a different layer thickness, I suggest scaling the STL files the appropriate amount. The strings that make up the surface of the balloon are a single filament thick, as well as the eight on the gondola. You might want to print the gondola raftless.
Print the balloon and gondola parts and glue them together. This is easiest with the balloon part upside down, supported in something like a cup or small bowl. Although the completed model can stand on its base, it might be nice to hang it from something.
Both parts should fit on a Makerbot. You'll probably get best results if you have a stepper motor extruder.
Balloon: 90.5mm x 90.5mm x 106.7mm tall
Gondola: 43.8mm x 43.8mm x 20mm tall