If one is using oil there is an argument about using previously used wicks. Some prefer to use new wicks every night as it is more respectful while others maintain that a used wick actually burns better and is therefore preferable.
Used wicks should not be disposed of in the regular fashion that one disposes waste. Because it was used for a mitzvah they should be disposed of with care. One can either burn the wicks or put them in a bag and then place the bag in the trash.