Now that someone's brought this up, what's the lowest output nodes won't reject now? Last I recall it was still at 3 satoshis/byte, so for a typical SW tx from my Electrum it's 141x3 = 423 satoshi.
Any transaction in which the value of the transaction is less than the amount you would pay in fees is rejected. The default dustRelayFee is 3,000 sat/kilobyte, so for a 1-input-1-output legacy transaction of 182 bytes, the minimum transaction is 546 satoshi. This number will be smaller for transactions using SegWit inputs or outputs. You can read the relevant parts on github here:
https://github.com/bitcoin/bitcoin/blob/master/src/policy/policy.cpp (Lines 16 - 29).
Very helpful, thanks! So it is 3 sats/byte anyway (though maybe actually less since 1 kb is > 1000 bytes?). Makes me wonder now how much is stuck out of circulation because of this.
I've never had the "opportunity" to send anything so small to be honest, although I can foresee that by the time I'll have some reason to do so, we'll already be taking these kinds of transactions off chain onto lightning channels.