If you receive 1 satoshi (0.00000001 bitcoin) in a transaction then adding it as an input to a larger transaction would add more than 1 satoshi to the transaction fee. This means the 1 satoshi shows in the total balance for your wallet, but in reality it is not worth anything to you because it would cost more than 1 satoshi to spend. In fact if you need to empty the wallet completely then the 1 satoshi is causing a loss.
So how small can a payment be while still adding value to your wallet?