Party switching has a long history. These are only the ones who, in more recent times, switched while they held national office (except for the very first on the list).
There are
plenty more listed here.
DEM to GOP
1962 Ronald Reagan (long before he ran for office)
1964 Strom Thurmond (while US Senator from South Carolina)
1965 Arlen Spector (while running for Philadelphia District Attorney)
1970 Jesse Helms (2 years before running as Republican for US Senate)
1972 Trent Lott (while running for US House of Representatives from Mississippi)
1973 Mills Godwin (Dem governor of Virginia 1966-70, elected as GOP governor 1974-78)
1973 Samuel Hayakawa (3 years before running for US Senate from California)
1975 John Jarman (while US Representative from Oklahoma, retired in 1976)
1981 Bob Stump (while US Representative from Arizona)
1981 Eugene Atkinson (while US Representative from Pennsylvania)
1983 Phil Graham (while US Representative from Texas)
1984 Andy Ireland (while US Representative from Florida)
1986 Richard Baker (while running for US Representative from Louisiana)
1989 Bill Grant (while US Representative from Florida)
1989 Tommy Robinson (while US Representative from Arkansas)
1990 Vito Fossella (while US Representative from New York)
1994 Richard Shelby (while US Senator from Alabama)
1995 Jimmy Hayes (while US Representative from Louisiana)
1995 Greg Laughlin (while US Representative from Texas)
1995 Mike Parker (while US Representative from Mississippi)
1996 Norm Coleman (while mayor of St. Paul, MN before becoming US Senator)
2000 Matthew Martinez (while US Representative from California)
2002 Virgil Goode (while US Representative from Virginia, became IND in 2000)
2004 Ralph Hall (while US Representative from Texas)
GOP to DEM
1972 Ogden Reid (while US Representative from New York)
1973 Don Riegle (while US Representative from Michigan)
1999 Michael Forbes (while US Representative from New York)
2009 Arlen Spector (AGAIN! while US Senator from Pennsylvania)