Is there any 'real' difference between the two? Michael Swan (
Practical English Usage) doesn't think so, claiming that "with some verbs, can is often left out without changing the meaning very much" and giving a few examples:
1) I (can) remember London during the war.
2) She can speak/speaks Greek.
3) I can't/don't understand.
4) Do/can you play the piano?
2) and 4) seem to be quite clear, we talk about an ability here (
can) which can be seen as a regular activity (
do/0).
I've given 1) and 3) a thought or two and finally arrived at this:
can may express an effort, thus (
no matter how hard I try) "I can't understand", (
my memory serves me good and) "I can remember London during the war.",
while the alternatives would read (
I was living there at the time so I can say) "I remember London during the war." and (
I don't speak Russian, obviously) "I don't understand."
This 'theory' of mine is more or less supported by a couple of examples taken from a BBC World Service Learning English article:
Do you remember the first time we sat under the stars, listening to Beethoven's Ninth?
Do you remember when we first ate wild mushrooms? ~ Yes, I remember.
I can't remember where I've put the spare set of car keys. Have you seen them?
(at least the last one works

)
Any ideas?
Thanks.