newbie,
This is an very old argument. They are in fact both correct.
"This is I" and "It is I" are grammatically correct because "I" is NOT in the object position. "I" is the complement of the linking verb "is".
"This is me" and "It is me" are also correct because they are commonly used in real speech by educated people everywhere.
Personally, I almost never use "This is I" or "It is I". It seems stuffy or redundant to me. However, I still think there use would be appropriate in some cases.
For example,
This is I who am speaking. instead of "This is me speaking."
It is I who am speaking instead of "It's me who is speaking"
In some contexts, in very formal writing for example, or perhaps when giving testimony in a court of law, you still may want to use "I" after the verb "to be", despite the fact that "me" is almost universal in informal contexts.