Depends on your situation. If you have a throwaway computer and some spare bandwidth, for instance, it will cost you precisely nothing. However, I don't recommend pushing transactions without fees. It could take days to get a confirmation, and it might just be dropped entirely from the network.

The fact is, reward subsidy is dropping fast, and is really all that is incentivizing miners to secure the network. Fees need to rise a lot in the future to replace the reward subsidy. Get used to it IMO. In the future, LN will probably be quite useful for these pocket change transactions.