If all you need is one quick project, most CAD packages have some sort of 30-day trial (always with a "personal use only" agreement, often with watermarks on the output, occasionally with no ability to save a file).
AutoCAD is a standard default for just about anything - a little intimidating at first, but the busy interface can be easily simplified and cleaned up to hide the advanced functions. LOTS of free tutorials. Somewhat constrained in ability to make organic shapes.
As mentioned, SketchUp is a handy little app for, as the name implies, sketching ideas up quickly - but can be done with attention to dimensions, etc. Definitely far from my favorite tool, but popular with beginners or those intimidated by full CAD programs.
My personal favorite for general design is Rhinoceros 3D CAD from McNeel and Associates. Although not a conventional CAD application, it has an incredibly short learning curve, an ability to create wonderfully intricate shapes of ALL kinds, and built-in rendering capability. Rhino also has lots of built-in solids analysis capabilities, such as detecting leaks in seams, heat distribution through solids, or weight/applied force through a structure.
A relatively-newer player in the CAD scene is Revit from Autodesk - supplying you with pre-built solid shapes and capable of analyzing just about any applied force or effect, but at a high learning curve.
One of the most popular 3D modeling programs available for free is Amapi. Full-featured modeling in a straight forward interface that is easy for beginners to pick up.
