Hi Hitesh,

You've definitely lead me down the right path.  What I've learned here is that when trying to update a field of the triggering record, through the use of a trigger, the record in question must be handled via the Trigger.new list/record.  Meaning, the use of the following block of code works, but not as expected:

            for (Contact newContact : Trigger.new) {
                if(newContact.Account != null){
                     newContact.Owner.Id =  newContact.Account.Owner.Id;              
                 }
            }

This code will only store the updated value in the newContact object.  Because the newContact object is just a copy (in memory only), and not a reference to the actual triggering record, itt will NOT update the actual record we want the trigger to update.  Instead, we'll need to work directly with Trigger.new.

I've included my code below.  Please, if there's a better way to do this, let me know!  I'm always interested in making my code better, shorter or just more efficient.

Thanks!

-Frank

//Frank Chang - 8/29/13
trigger OnLeadConvertSyncOwnerToAccount on Contact (before insert, before update) {
    if (Trigger.isBefore) {       
        //Create an empty set of Id objects.
        Set<Id> ContactIDs = new Set<Id>();
        if (Trigger.isInsert || Trigger.isUpdate){  
            for (Contact newContact : Trigger.new) {
                //Loop through all the "new" contact records affected by this trigger and add them to
                //our Set of Id's.
                ContactIDs.add(newContact.Id);  
            }
            //Just making sure that our Set contains at least one Id value.
            if(ContactIDs.size() > 0){
                //Execute a SOQL query using our Set of contact Id's to retrieve additional (related)
                //info. Store the retrieved list of contacts.
                List<Contact> ContactsToUpdate = [SELECT Id, Name, Account.Owner.Id
                                                  FROM Contact
                                                  WHERE Id IN :ContactIDs];
                if(ContactsToUpdate.size() >0){
                    //If there are Contact records to update, create a hash (Map) based on the Id's of
                    //the current contact and the id of the current contact's Account's Owner Id.
                    Map<Id, Id> contactsAndOwners = new Map<Id, Id>();
                    //Populate our hash with data
                    for(Contact currentContact : ContactsToUpdate){
                        contactsAndOwners.put(currentContact.Id, currentContact.Account.Owner.Id);
                    }
                    //Using the hash set the triggering record's owner id field. It has to be done
                    //this way because the only way to update the triggering record's fields is to 
                    //use the Trigger.new list.
                    for (Integer i = 0; i < Trigger.new.size(); i++) {
                        if(contactsAndOwners.get(Trigger.new[i].Id) != null){
                            Trigger.new[i].OwnerId = contactsAndOwners.get(Trigger.new[i].Id);
                        }
                        system.debug(contactsAndOwners.get(Trigger.new[i].Id));
                    }
                }
            }            
        }
    }
}