No is used to answer questions, both alone and in certain phrases:

Avrai il tempo per uscire stasera?

-No, non credo.

-Credo di no / Temo di no / Spero di no / Mi sembra di no / Direi di no

I don't think so / I am afraid not / I hope not / I don't think so / I would say not

Perché no?

Why not?

No is also used in sentences to sum up a negative alternative:

Ma vuoi venire o no?

But do you want to come or not?

Dimmi se ti piace o no(Note the R1–2 alternative: Dimmi se ti piace o meno).

Tell me if you like it or not.

If no applies to one particular word, it usually follows that word, e.g.:

Tommaso è d'accordo, ma Elena no.

Tommaso agrees, but Elena doesn't.

Andrei volentieri al Luna Park, ma con te no (cf. ma non con te)

I would gladly go to the Amusement Park, but not with you.

Avete tutti ricevuto l'invito? Io no.

Have you all received the invitation? – I haven't.

Sono tutti eligibili, studenti e no.

All are eligible, students and non-students.

A common, but less correct, alternative is to use non:

Sono tutti d'accordo, politici e non.

All are in agreement, politicians and non-politicians (OR politicians and others).