I recall Merlene Ottey, who represented Jamaica (1980, 1984, 1988, 1992, 1996 and 2000) and Slovenia (2004). She obtained 9 medals representing Jamaica: 3 silver and 6 bronze.
I also recall the cross-country skier Johann Mühlegg, who competed in the 1992, 1994 and 1998 Winter Olympics representing Germany and the 2002 Winter Olympics representing Spain (he got medals, but was later on disqualified after testing positive on drugs).