I'd say 'candy machine' or 'snack machine' as AE speaker. 'Snack machine' might be used more when there are things in addition to candy available in the machine.

I have also heard 'vending machine'.

They're called "vending machines" - here's a link to some pictures.

One more vote for vending machines (Canada)

I agree with maxxxpf:
The general (and therefore most widely used) term is "vending machine"
"Candy machine" is when nothing but sweets is in the machine.
"Snack machine" is used but less often than vending machine.

Nichts von dem bisher Gesagten wird in Zweifel gezogen, aber da generieren sich ein paar Fragen in mir:

- ein Getränkeautomat wäre auch eine vending machine

- ein Zigarrettenautomat wäre auch eine vending machine

Soll heißen: wie macht man da die Unterschiede klar?

getränkeautomat = drink machine (wir würden darum nicht kummern, 'drink vending machine' zu sagen)

süßigkeitenautomat = candy machine (wir würden darum nicht kummern, 'candy vending machine' zu sagen)

Usw. Alles klar?

Have never seen a vending machine that had only candy bars, no chips, nuts, gum. Have never heard anyone call a vending machine a candy machine or snack machine.

A soft-drink machine is also often just called a vending machine.

Are cigarette vending machines even legal in the U.S?