State verbs are verbs that cannot be used in the continuous form.
That means that for instance if you normally would use the present continuous, when you use a state verb, you have to use the present simple.
Here is a list:
to be (être) He is at home at the moment.
to believe (croire) Now I believe you!
to belong to (appartenir à) This bag belongs to me.
to consist of (consister en) What does the course consist of?
to contain (contenir) The box contained old books.
to depend on (dépendre de ) It depends on the weather.
to deserve (mériter) He doesn't deserve the gold medal.
to exist (exister) Santa Claus doesn't exist.
to forget (oublier) He never forgets his keys.
to hate (détester) I hate liars!!
to know (know) I have known her for 10 years.
to like (aimer) I like listening to music.
to love (aimer) He has always loved her.
to matter (être important) It doesn't matter.
to mean (vouloir dire /signifier) What does this word mean?
to need (avoir besoin de) I need a coffee!!
to own (posseder) He owns a Ferrari.
to prefer (préférer) She prefers going to the mountains.
to realise (se rendre compte) I realise that it isn't easy.
to remember (se souvenir) I remember reading this book.
to resemble (ressembler) He resembles his father.
to seem (sembler) She seems very friendly
to suppose (supposer) I suppose that you want to go home.
to understand (comprendre) Now I understand what he's talking about!
to want (vouloir) I want to go to the cinema.