As a noun:
* Could you do me a favor and grab the mail on your way in? (Asking for help)
* She asked for a favor, but I wasn't able to help. (Request for assistance)
* The judge showed the defendant no favor. (No special treatment)
* He was in her favor after she helped him out. (Feeling positively towards someone)
As a verb:
* I favor the blue dress over the red one. (Prefer)
* The coach favors his star player. (Show partiality towards)
* The wind favors us, we should set sail. (Be advantageous to)
Note: "Favor" can also be spelled "favour" in British English.