I am thinking of Ally McBeal in particular. For the entire run of the show the opening credits generally had clips of a character and the name of the actor that plays them. The final two actors (Peter MacNicol for the entire run, Gil Bellows until season 4 and Robert Downey Jr from there on) are billed differently. It says 'With Peter MacNicol and Robert Downey Jr', accompanied with the respective video clips for example. 

While the characters are important, they are by no means the most central. In fact, not one of the actors billed as 'with' appear in every episode! Why are they billed differently?