I often hear how people from the United States pronounce "twenty" as "twonny" in movies, etc. Why? Is this an alternative pronunciation?
I'm not a native speaker but I've been learning mostly American English for a long time now and the so-called flapped t is widely used by American English speakers in fluent speech.
That's probably what szx heard. So twenty becomes \'twɛni\ to rhyme with 'penny'. But my guess is that in really fast speech it can even become more like tw'nny resulting in something like \'twɐni\ or \'twʌni\ which can probably be transcribed as 'twonny'.
The Oxford Advanced American Dictionary:
twenty number/ˈtwɛnti; ˈtwɛni; ˈtwʌni/
For more information on 'flapped t' refer to Wikipedia:
The cluster [nt] can also be flapped/tapped; the IPA symbol for a nasal tap is [ɾ̃]. As a result, in quick speech, words like winner and winter can become homophonous.