Can you destroy a spider web on shabbos if you simply do not want it around (you consider it unseemly)?
Rabbi Yehoshua Neuwirth (1989) in section (23:9), “Housekeeping and use of domestic facilities on Shabbos and Yom Tov,” codified the following halachos. “Cobwebs on furniture or some other movable article may be removed, provided that this is done not with one’s hands, but with a broom or some other instrument. One should not remove cobwebs from the walls, the ceiling, or any other part of the home, both (1) because the cobwebs themselves are muktzeh and (2) because doing so is analogous to the forbidden activity of detaching something which is connected to the ground. If one finds a spider, one is of course not allowed to kill it on Shabbath or Yom Tov.” Apparently, the Sephardic viewpoint is slightly different, as Rabbi Abraham HaCohen Soae (2005) noted the following: “It is permitted to gently remove a spider web from the wall on Shabbat, provided one is careful not to kill the spider on Shabbat. Other poskim forbid removing a spider web on Shabbat because it is included in the forbidden act of uprooting, tolesh min hamechubar.”