The "I" and "ME" Confusion

We get this so often.. I read this on social networking sites where they post dozens of pictures of them with someone else.. And then, tragedy strikes... They post the comment... "Sam and I".. Huwat!!!???? Yeah, yeah.. back in high school we were taught to use I when joining it with another noun or pronoun and "AND" but the lesson does not just end there.

The concept of a conjunction is to join two of the similar idea. Case and point.
He and I are going to the beach. (correct)
Separate the two:
He is going to the beach.
I am going to the beach.

This was written by John and I. (incorrect)
Separate the two:
This was written by John.
This was written by I (?!?!?!)
You'd, then, write it this way:
This was written by ME.
ergo.. the sentence would then become:
This was written by John and me.

Think about it... it's a peeve of mine and it starts to get irritating when you a whole lot of people doing it.

Same as for comments under pictures... It's not "___ and I" but, "___ and me."