You can find such a list, for instance, in the Penguin Handbook.
Note: as of December 2014, the above link does not work.
There is a copy of The Brief Penguin Handbook here;
the Verbs Followed by Gerunds or Infinitives section is here.
The only way to know is to memorize which verbs are followed by gerunds and which are followed by infinitives. The relevant categories are:
Verbs Followed by Infinitives
Most verbs are followed by infinitives.
If the verb is not found in the list below, it is probably followed by an infinitive.
Verbs Followed by Gerunds
The verbs in the following table all need to be followed by gerunds.
The students don’t enjoy going over the same rules again and again.
- admit (to)
- be accustomed to
- be used to
- can’t help
- feel like
- get used to
- keep (on)
- look forward to
- (not) mind
- put off
Verbs Followed by an Object Before the Infinitive Verb
I advise you to go to school early today.
- *would like
*Some words can be used without an object as well as with an object.
I want him to go. I want to go.
Verbs Followed by Either Gerund or Infinitive
Sometimes the meaning changes according to the verb used.
He doesn’t remember giving the homework to Mr. Young.
He didn’t remember to give the homework to Mr. Young.
- can (not) bear
- can (not) stand
Verbs Followed Only by the Simple Form (no “-ing” or “to”)
Four verbs are called causative verbs.
They are followed by an object; the verb after the object is always in the simple form:
- let: They let him go on the trip (instead of “let him to go”).
I let him take my book home for one night.
- make: We made her do her chores first.
I made my sister cry.
- help: She helped her finish her homework.
I helped him find the bookstore.
- have: The teacher had him stay after school.
I had my teacher explain the answers.
Verbs Followed by Either the Simple Form or the Gerund (no “to”)
Some verbs are called verbs of perception and are followed by either the simple form or the “-ing” form.
I see him going.
- notice: I notice him run to school every day.
I notice him running to school every day.
- watch: I watch him struggle with his homework.
I watch him struggling with his homework.
I hear him singing.
Others including: look at, observe, listen to, feel, smell.