i don't forget you vs i will not forget about you

Some examples from the web:

• No, I don't forget you when I need you.
• I know but don't forget you are the law here.
• You want me like this so that I don't forget what I owe you.
• No, I don't think you forget.
• No, I don't suppose you did forget.
• No, and I don't think you'll forget me, either.
• I don't want you to forget what you've seen here today.
• I don't think you can forget I think it would've been a good idea if Amy decided not to have a baby.
• I don't want you to forget about it or pretend it never happened.
• So I don't forget the birth of my daughter.
• I don't forget those who stand with me.
• 'Cause I don't forget eyes like yours.
• Write down my dreams so i don't forget 'em.
• I don't forget my debts, Mitch.
• There are a few things I don't forget so easily.
• So I don't forget what it looks like when you're at work.
• It's not like I don't forget everything else I've done in my life, I mean.
• You know, you're the one who's always telling me that I should write stuff down so I don't forget it.
• I don't forget a single thing I see.
• I want to write that down so I don't forget.

Some examples from the web:

• I will not forget about the loyal cooperation and the commitment to Europe that he showed just because he is no longer in power.
• Firstly, we must show the Commission, the Council and the Member States that this House cannot and will not forget about this serious incident.
• Let's not forget about the community college student.
• Let's not forget about the YouTube videos.
• We should not forget about the Hungarian menace.
• And let's not forget About Lauren Tanner.
• Then again, let's not forget about the other people.
• Do not forget about help to the sufferring farmers.
• You better not forget about it later.
• But let's not forget about repairing the Batmobile.
• We should not forget about our partners in the dialogue with Cuba.
• Therefore, we must not forget about the energy mix.
• One thing we must not forget about is having a correct balance.
• I can never forget about you.
• I never forget about you and Moe, Harry.
• I thought being with Jingping could make me forget about you.
• We won't forget about you.
• Thank you so much, I won't forget about you.
• Uncle Mel won't forget about you, handsome.
• And we didn't forget about you either, Mr.Froment.