When we talk about something that is happening as we speak.
Watch me, Mum, I can stand on one leg.
Before passive
CDs can now be copied easily.
When the meaning is "know how to"
Can you cook?
Talk about single achievement rather than general ability in the past
Sue could / was able to play the flute quite well <-- general ability
She swam strongly and was able to cross the river easily, even though it was swollen by the heavy rain <-- achievement
In negative sentences
I tried to get up but I couldn't move
With verbs of the senses and thinking
senses: feel, hear, see, smell, taste
thinking: believe, decide, remember, understand
I could remember the crash, but nothing after that
When it means "the only thing"
usually with phrases: the only thing/place/time
All we could see were his feet
Say that something almost happen
I could nearly touch the ceiling