Bon Ami is what I often use, and the best thing I've found is sold on Q, called Bio Cleaner.
This stuff doesn't scratch, but cleans of scuff marks better than anything I've found.
HonnyBrown is right as well, about the elbow grease.
And your Corelle, the Bio Cleaner will clean them up some too, but I've found that after some time, those marks are there to stay. My Corelle is over 30 years old, and some of those marks are permanent after that long.