Originally Posted by Rlyss

Without wanting to get into any e-penis discussion, I thought I'd just point out that what you're talking about here is a form of hyper-correction. People have realized that there are times when saying 'me' is incorrect, but they over-compensate.

'Bob and I went to the store' is correct.
'*Bob and me went to the store' is incorrect.

'Come to the store with Bob and me' is correct.
'*Come to the store with Bob and I' is incorrect.

The best way to tell whether you're saying it correctly is to take Bob out of the sentence. So 'I went to the store' and 'Come to the store with me' are both correct, but '*Me went to the store' and '*Come to the store with I' are both incorrect.