"Forget" and "forget about"

Lothar has asked a very good question: what's the difference between forget and forget about?

Forget about is used with a couple specific senses of forget. In the following senses, the use of about is optional.

When forget is used to mean "to stop thinking or caring about (someone)":

He was once a famous actor, but now most people have forgotten (about) him.

You shouldn't forget (about) your old friends.

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When forget is used to mean "to stop thinking or caring about (something) on purpose":

We need to forget (about) our differences and learn to get along.

“I'm sorry I'm late.” “That's OK. Forget (about) it.” [=don't worry about it]

Forget about finding a way to escape—there's no way out of here.

I had almost forgotten about my car accident last year.

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About can add some emphasis when something specific is forgotten, but sometimes the structure of the sentence changes:

I forgot to pay the bill. = I forgot about paying the bill.

To emphasize even more:

I forgot all about paying the bill.