Question:
Can one move a fan on Shabbos?
Discussion:
A fan is considered, by many Poskim, to be a kli shemilachto l'issur (an object whose primary use is prohibited on Shabbos); therefore it can be moved if its' place is needed or if you are using it for a permitted usage. This means that if the fan is blowing on a person and he no longer wants it to be blowing on him he can move the fan. This falls under the category of needing its' place because when the fan is blowing in his direction it is stopping him from using that spot comfortably.
It is also permissible to move the fan so that it is blowing on you as well since this is considered using it in a permissible way. Rav Moshe zt"l however, has an interesting view on this matter (O.C. 5:23, 22:22). He holds that a fan is actually a kli shemilachto l'heter (an object that has a permitted usage) because the action of the fan is not prohibited (i.e. the spinning of the blades), even though the cause of the spinning (the electricity) is something prohibited. So, according to Rav Moshe zt"l one would be allowed to move the fan for any reason. Care must be taken to make sure it is not unplugged. This is only if the fan is functioning; if the fan is off then it should not be moved at all unless the spot the fan is occupying is needed.
Another question is can one make the fan oscillate assuming that one does not have to press a button or use electricity to do so? There is a difference of opinions regarding this. Rav Auerbach zt"l says that it is permissible to do so even if a small amount of electricity since it is undetectable to human senses (Shulchan Shlomo 308:34). Rav Elyashiv zt"l says that it would be prohibited unless no electricity was used at all (Meor Hashabbos 14:117)
Summary:
One is permitted to move a fan that is functioning on Shabbos. However, there is a dispute in regards to making the fan oscillate on Shabbos. Rav Elyashiv zt"l says one cannot make it oscillate and Rav Auerbach zt"l says one can make the fan oscillate on Shabbos.