They like each other, but their feelings do not surpass those of friendship. It was made clear at the end of Avatar: The Last Airbender that Zuko liked Mai as the were seen sharing an intimate kiss and hug before his coronation. Katara and Aang also get together at the end, sharing a deep, passionate kiss that is engaged by Katara. Aang and Katara eventually got married and had three children together and Zuko has been known to have a daughter and a grandson, so it is safe to say that Katara and Zuko never had romantic feelings for each other.