Some verbs may take either Infinitive or Gerund form.

forget + to-inf (= forget to do sth.) He forgot to switch off the monitor.

forget + -ing form (= forget a past event)

I'll never forget meeting Bill Gates in 2002.

remember + to-inf. (= remember to do sth)

I hope you'll remember to turn off the equipment.

remember + -ing form (= recall a past event)

I don't remember him leading this project.

mean + to-inf. (= intend to)

She means to start a new life.

mean + -ing form (= involve)

I won't take the job if it means moving to Scotland.

go on + to-inf (= finish doing sth. and start doing sth. else)

They finished one project and went on to create another.

go on + -ing form (= continue)

She went on writing till the morning. regret + to-inf (= be sorry to)

I regret to inform you that your services are no longer required.

regret + -ing form (= have second thoughts about sth. already done)

He regrets misbehaving.

would prefer + to-inf (specific preference)

I'd prefer to see you in private.

prefer + -ing form (in general)

I prefer working on my own.

try + to-inf (= do one's best; attempt) Let’s try to update our software.

try + -ing form (= do sth. as an experiment)

Try changing these parts. I think it will work much better without them.

want + to-inf (= wish)

I want to finish this experiment as fast as possible.

want + -ing form (= sth. needs to be done)

This device wants upgrading.

stop + to-inf (= pause temporarily)

He stopped at the garage to have the tank filled.

stop + -ing form (= finish; cease)

He stopped behaving foolishly.

be sorry + to-inf (= regret)

I'm sorry to tell you your project has been postponed.

be sorry for + -ing form (= apologise for)

She was sorry for causing troubles during the procedure.

hate + to-inf (= hate what one is about to do)

I hate to cut in, but you must see the project leader.

hate + -ing form (= feel sorry for what one is doing)

I hate causing you so much inconvenience.

be afraid + to-inf (= be too frightened to do sth.; hesitate)

She was afraid to conduct the experiment.

be afraid of + -ing form (= be afraid that what is referred to by the -ing form may happen)

When they create a new project, they are always afraid of being mistaken.