The usual list is the Australian dollar, the New Zealand dollar, the Canadian dollar and the Norwegian krone, with several emerging market currencies behaving the same way. The link runs through terms-of-trade: higher export prices mean higher national income, better fiscal revenue and often a stronger rate outlook.
The correlations are real but unstable. The aussie tracked iron ore and Chinese demand closely for years, then decoupled when domestic rates diverged from the rest of the world. Treating the relationship as mechanical is how traders end up short a currency that is rallying against the commodity it is meant to follow.
Because commodities themselves are dollar-priced, these currencies also carry a built-in inverse dollar exposure, which is why they feature so prominently in risk-on-risk-off discussions.
Example: iron ore rises 20% over a quarter and AUD/USD gains 3%. A trader long AUD and also long a mining equity is holding one bet twice, not two diversified bets.
Related: petrocurrency, terms-of-trade, aussie, currency-correlation