The subjunctive is used in a subordinate clause when the main clause expresses doubt or uncertainty on the part of the speaker.

Certain - Indicative

saber, es verdad, es cierto, seguro que, no dudar, no negar que, cierto que

Not Certain - Subjunctive

creer, pensar que, quizás, tal vez, no saber, no creer, no pensar que, dudar, negar que, no es verdad, es posible, es probable que, etc.

The expressions below need a que before using the subjunctive.

es posible que - it's possible that
puede ser que - it could be that
es fácil que - it's easy that
es difícil que - it's difficult that
es probable que - it's likely that
es imposible que - it's impossible that

Es imposible que gane el examen.
It's impossible that I will pass the exam.

Es probable que el tren llegue con retraso.
It's likely that the train will arrive late.

Paramos porque puede ser que venga otro carro que no veamos.
We are stopping because there may be a car coming that we do not see.

No creo que vuelva antes.
I don't believe that I return before.

The expressions below do NOT need a que before using the subjunctive.

quizás - maybe
tal vez - perhaps
a lo mejor - perhaps
posiblemente - possibly

Tal vez nos veamos mañana.
We may see each other tomorrow.

Quizás María Luisa tenga mucho quehacer.
Maybe María Luisa has a lot to do.

Quizás tengamos un examen mañana.
Perhaps we have an exam tomorrow.

Tal vez el programa empiece a las cinco.
Maybe the program begins at 5.

The most common verb used to express doubt is dudar (to doubt).

Marcos duda que el jardinero trabaje hoy.
Marcos doubts that the gardener is working today.

El médico duda que nos sintamos enfermos.
The doctor doubts that we feel sick.

Note: Sometimes, doubt is expressed and the subjunctive is not used. This is the case with the following:
creer, parecer que, pensar, no es dudoso

Creemos que ella es bonita.
We think that she is pretty.

Me parece que empieza un buen resfriado.
It seems like you are starting a good cold.

Yo pienso que es muy interesante.
I think it's very interesting.

Note: Just because a sentence includes a que, that does not mean that one will use the subjunctive mood. Doubt requires subjunctive while certainty requires indicative.

Doubt requires subjunctive

Es dudoso que + subjunctive
No es cierto que + subjunctive
No creo que + subjunctive
No pienso que + subjunctive
No parece que + subjunctive

Certainty requires indicative

Es cierto que + indicative
Es verdad que + indicative
Es evidente que + indicative
Es obvio que + indicative
No es dudoso que + indicative
No dudo que + indicative

Example sentences using the indicative.

Es cierto que Marisa viene hoy.
Es verdad que Julia y Marisa llegan hoy.
Es evidente que estas enojada.
Es obvio de que Juan ama a Julia.
No dudo que tengo que ir a clase.