Examples

Forget + to - inf

1. I have to leave now. I forgot to lock the door when I went out.

2. She couldn't reach Susan yesterday, she forgot to invite her. 

3. She keeps forgetting to bring his book bag. 

4. They forgot to warn us about payment. 

Forget + ING form

1. We will never forget meeting our boss for the first time.

2. I will never forget wearing gloves before playing the snow.

3. He will never forget spending whole day with his relatives.

Remember + to - inf

1. Please remember to buy spices on the way home. 

2. Did you remember to estimate the cost for the coming quarter ? 

3. Why do I never remember to ask him?

Remember + ING form

1. I don't remember ever visiting this Museum before. 

2. I don't remember losing my glasses. 

3. I remember going to the beach when I was a child

Go on + to - inf

1. He greeted with guests and went on talking to Maria. 

2. She took a picture and went on wandering the town. 

3. They went on revising the vocabulary.

Go on + ING form

1. She smiled and went on to speak of various family happenings. 

2. She went on without waiting, to see what decision they would come to. 

3. He went on to describe hurriedly the personal conflict with his friend.