There are always things about practicing, equipment, playing a tune, etc. where you go "Ah! I wish I knew that sooner!" I've been playing saxophone for 24 years now and I just found this out a couple years ago: Don't Use Petroleum Based Cork Grease.
This is most "premium" or "special formula" cork grease that you find in the Chapstick-like tube. The reason is that all of these are petroleum based. Petroleum is fine for your cork (kind of); it lubricates and protects it from too much moisture. Petroleum is NOT fine for the glue that keeps the cork on your neck. Anyone who has ever had to have the cork on your neck replaced has, at one point, watched perfectly good cork just fall off the neck with little to no sign of wear. The petroleum in the Chapstick-cork grease seeps into the cork and dissolves the glue.
It's important to remember that cork is a natural product that comes from trees. It needs some moisture to stay resilient, but not too much or it will break down. These are the ones I have used so far that seem to work really well:
Note that everyone will have to replace their cork at one time or another. I prefer using shellac to attach the cork vs rubber cement. I like the sound and I believe the shellac holds up against moisture better than rubber cement. I'd love to hear anyone's comments or experiences on this.