I want to create a dropdown navigation. I drew this sketch:

I already tried a spinner, but I don’t want that combobox, only that list, which shows on the button click.
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I am assuming you are working on an API below 11. The Dropdown spinner is available from API Level 11 with the Actionbar. But you could use Actionbar sherlock. Download the Demos( as source from Github or as an app from the play store). The actionbarsherlock implements dropdownspinners. It should look like this:
You can get the Library from:
https://github.com/JakeWharton/ActionBarSherlock