When determining the load bearing capacity of any structure, you'll need to take into account several different factors:
- Acceptable deflection
- Maximum allowable bending stress
- Column compressive and buckling strengths
For calculating deflection, @rob's suggestion of using the Sagulator is a good start. You don't need to have an in-depth grasp of all the engineering concepts going on behind the scenes to get a 90% answer. The Sagulator is simply inputting your furniture's dimensions into a beam deflection equation and spitting out the answer. These equations rely on the assumption the material remains within its elastic limit. You can test this in the Sagulator by inputting a 5,000 lb loading for a 1/2" thick pine shelf. The deflection shown will be greater than the length of the shelf, since the equation doesn't factor in the ultimate strength of the material.
Maximum bending stress allows you to calculate how much loading your furniture can take without breaking. The maximum load a horizontal beam can sustain depends on the span, how the load is applied, how the ends are supported, the material, and the cross-sectional geometry. Luckily, there are several online resources like Engineer's Edge and the Engineering Toolbox that can help with generalizations, so you don't have to derive each condition.
For a uniform loading on a beam with fixed-fixed end conditions (that means the joints are connected at each end by glue, or at least by more than one fastener), the maximum bending stress will be located at the ends, at a magnitude of
sigma = M*y/I
M is the maximum moment,
I is the cross section moment of area
y is the distance from the neutral axis.
For a rectangular cross section, , and I = 1/12*b*h^3, where h is the beam thickness, and b is the beam width. The y is simply h/2.
You can calculate your maximum M with this calculator.
The maximum allowable stress (or Modulus of Rupture) for many wood species can be found by searching Google for wood material properties.
Don't forget your safety factor on this part!
Column compressive and buckling strengths won't really play into your design considerations unless you're planning on using long, spindly legs. With 4x4 legs, you won't have this problem. With thinner legs, you can calculate the critical centric loading (aligned with the axis of the leg, applied in the center of the leg) with the following formula:
E is the material modulus of elasticity
I is the area moment of inertia of the leg cross section,
K is the column effective length factor,
L is the unsupported length
For unsupported legs attached only at a table apron or the top of your bench, K will be 2, since it's essentially a fixed-free end condition. For a legs connected with a brace at the bottom, K will be closer to 0.5, and column compressive strength is more of a factor.