Question
Hi, I've removed a dead and cracked branch (about 8inches in diameter) from my dogwood -- do I need to seal the remaining open 'stub' of healthy wood with anything to protect the tree?

Answer
Prune the branch back to the branch collar (there will be a slight difference in the taper of the branch next to the main trunk.) do not cut all the way flush with the trunk but leave a 1/4 inch or so. The tree will heal over by itself--Do Not put sealing paint on the wounds this will slow the healing process.  
Here is a web link that show this pruning method.
http://www.umext.maine.edu/onlinepubs/htmpubs/2169.htm