The yen and the Swiss franc have been the archetypes, with the euro joining them during its negative rate years. Being a funding currency has consequences: it tends to be weak while the carry is on, then strengthen sharply when risk is cut, because closing positions means buying it back.
This is why the yen often rallies on bad news that has nothing to do with Japan. It is a position effect, not a judgement about the Japanese economy. See safe-haven-currency for the overlapping but distinct idea.
Example: with Japanese rates at 0.3% and Mexican rates at 10.5%, a yen-funded peso position earns about 10.2% a year. If the yen gains 12% in a month, that year of carry is gone and the position is down roughly 2%.
Related: carry-trade, carry-unwind, yen-cross