verb
BAD : 'He went to the doctor's yesterday.' - 'Yes, I can remember. He looked very ill.'
GOOD : 'He went to the doctor's yesterday.' - 'Yes, I remember. He looked very ill.'
BAD : Can you remember me? I used to sit at the back of your class.
GOOD : Do you remember me? I used to sit at the back of your class.
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When remember means 'bring the memory of a person or thing into your mind (i.e. recall ) then can/could is usually optional: 'I (can) still remember the sad look on her face.' Use can/could to suggest effort: 'I just can't remember how the film ended.' 'I wish I could remember their address."
When remember means 'have or keep the memory of a person or thing in your mind', it is usually used WITHOUT can/could : 'I hope you still remember me.' 'I'll always remember the night we first met.'