Which countries back their money by gold?

Answer 1

Although the last vestiges of the gold standard disappeared in 1971, its appeal is still strong. Those who oppose giving discretionary powers to the central bank are attracted by the simplicity of its basic rule. Others view it as an effective anchor for the world price level. Still others look back longingly to the fixity of exchange rates. However, despite its appeal, many of the conditions which made the gold standard so successful vanished in 1914. In particular, the importance that governments attach to full employment means that they are unlikely to make maintaining the gold standard link and its corollary, long-run price stability, the primary goal of economic policy.

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Answer 2

To my knowledge, none of them do.

After WWII; many currencies were backed by the US Dollar, which was backed by gold, this is no longer the case.