In some cases, a design code (or common sense) tell you specifically that gravitational loads should be included. Typical in structural applications, for example.
Otherwise, you should be able to come up with an order-of-magnitude type value of stresses due to the weight of the object being analyzed.
Consider then, what the uncertainty is on your applied loadings. For example, if your applied loads are assumed, or based on some probabilistic analysis, they aren't going to be accurate to 8 decimal places. If you get, say, 10,000 PSI stress based on a load that could actually vary +/-25% or more, and estimate that gravity loading gives you 100 PSI, there really isn't much point in calculating gravity loading.
I agree with JStephen. See how much stress your gravity load alone gives and compare it with the stress obtained by applied full-scale load. Also see how much your part/assembly weights and how it is supported.