Caine has said in Empire magazine he would come back as Alfred even if it was a reboot.
I would be very happy with that. With these quickie reboots its hard for actors in the supporting parts to really make the characters their own in the little time they have. If Judi Dench could continue as M past the Bond reboot why not similar in Superhero films.
In future Spider-man sequels it would be nice if J.K. Simmons returns as J. Jonah Jameson.
It has happened before. Noel Neill was the first actress to play Lois Lane in live action for the Superman serials. Later when the first Superman series began it was a full reboot with new cast. But after the first season new Lois Lane actress Phyllis Coates left the show. So the producers brought back Noel Neill to the part and she continued for the rest of the series.