The solution of pgschk works great, but has one major problem: You cannot move the mouse outside and work outside of wine. For example, if a wine application is opened which doesn't allow to control the window, if you click in firefox search, you cannot type with your keyboard.
But there is also another solution, which is more general, as it works not only for wine, but also for other applications (as for example some java apps) which need fullscreen: Enable 'legacy fullscreen' in compizconfig-settings-manager.
Install the compizconfig-settings-manager, if not already installed
$sudo apt-get update && sudo apt-get install compizconfig-settings-manager
Open the compizconfig-settings-manager (can also be found in the unity lens by searching for 'compiz')
Click on the tab 'Advanced Search', which can be found below 'Categories' and 'Settings'
A list of Plugins will be shown. Select 'Workarounds'
Enable 'Legacy Fullscreen Support' (currently the second item in the list)
Restart your application in fullscreen and enjoy a screen without the unity bars :-)