MakerBot Print is our newest print-prepration software, which supports native CAD files and STL assemblies,
allows you to interact with all your printers via the Cloud, and many other exciting new features.
One of the most important things here is to know your printer - Some printers handle overhangs better than others. You often hear that anything more than a 60 degree angle from the horizontal needs to be supported, but I've used printers that can achieve much more than that. If you search Thingiverse for "overhang" you'll find plenty of test pieces where you can find out what your machine is capable of. Your results will depend on the material and the printing profile. For example, i got better results printing PETG when I increased my cooling.
If your overhang is supported on two sides, like a bridge, then you can get much bigger overhangs - you'll need to look at the bridging settings in your slicer.
From the design point of view, it's always a good idea to try to "design out" overhangs. Sometimes this can be as easy as printing the model from another side, but often the simplest solution is to make the piece in two parts.
Hope this helps!