The last two actors I chose were lesser known to many I think. Here is a five move answer but I'm sure it can be done in fewer: 1. Lithgow to Eddie Murphy in Shrek; 2. Murphy to Robert de Niro in Showtime; 3. de Niro to Cuba Gooding Jr. in Men of honour; 4. Gooding Jr. to Lawrence Fishburne in Boyz in the Hood; and 5. Fishburne to Maria Bello in Assault on Precinct 13 (speaking of bad remakes!).
Next up, a couple of actresses:
#4 Lucy Liu to Bridget Moynahan