Unless you are the mining pool and you mine your own transaction - then you can set the fee to zero. Recently there were some transactions with 0 fee... 

nout

In te past zero fee transactions were possible. Currently I think nodes default configuration rejects that kind of transactions. 

I'm assuming that the fee amount is derived from the difference of the transaction inputs minus the outputs, and therefore could be set to an arbitrary amount.

captain_stacks

In electrum you can set it lower than 1sat/byte.

I've been tempted to try it at 0.2, but I need to look into more what will happen if it doesn't go through

Sometimes I do transactions at 1.1 just to push in a little. Haha

2bithits

найди первый кошелёк. 0 ставить можно. 

selfish_gene

bitcoin

I know most clients don’t let you set it lower. But is that a requirement or just a UX choice?