A lot of times, it would be considered negligible and disregarded. Example: Hanging a weight from a cable, people don't usually factor in the cable weight.
Often with geotechnical work (footings, piers, piles, etc.) the weight of the soil displaced is approximately the weight of the concrete placed, and, the weight of footings, etc. is ignored. In addition, the soil on top of the footing is often ignored because the soil already has the surcharge of these materials above the founding level.
Waterbottle7:
Answer your own question. Does the self weight effect the stresses, failure mechanism, or some such, at the location you are considering in your analysis? If it does, then include it. As others have suggested if you have a 1000kip load and the supporting member weights a few hundred pounds, then the inclusion of the self weight may not make a big difference in the final results. You have to learn to use some engineering judgement, if you want to pretend to be an engineer.