The most obvious way to me would be to use the Google AJAX Language API. http://code.google.com/apis/ajaxlanguage/
Using a custom widget you can retrieve the text-to-translate from an MxObject, translate it using Google and display it in a new textarea. There are any number of different ways you can set up the domain model to accommodate this.
I haven't used Google Language myself, but the examples at http://code.google.com/apis/ajaxlanguage/documentation/#Examples look pretty straightforward.
Currently you can use i18n to translate any field there is. While tricky it can also be used in custom widgets but there is no way to reuse your already made translations so there is no such thing as automatic translations, these will have to be done for each project for each language. but as Karol said the functionality of batch translation does help a lot.
Writing/ modeling an action which pushes some data in a webservice and retrieve a translation back should not be to hard. It would not surprise me if either Babelfish or Google have such services available .
While the application and Mendix provide translation support, the database is not designed to support multiple languages 'by nature'. You can discuss about the need for that and the market for localized and translated data, but it will always exist, as your question proves.
A solution can be that you copy the text fields from entities by creating a Localised Entity in parallel. E.g. Employee and LocalisedEmployee with reference both association (1:1). Add an Iso language id and filter on that id when displaying or entering data. Be sure to create the entities at the right time.
If you want to leave the rest of you app the same, write eventhandlers for every field and make the field virtual by adding microflows, but that can be an extensive job. Check the performance before.
what exactly do you mean? as far as I am aware automatic translation does not exist as such in mendix - just batch translate which you have to define yourself see the following forum entry: https://forum.mendix.com/questions/709/Automatic%20translation
I don't think you should trust Google Translate or Babelfish to translate your project. Otherwise you'll get very bad translations. Instead, your customer could provide you the correct translations. And you can use batch translate to translate all the text.
When you do not know the language automatic translation tools are useless. You always have to correct the text.
See article: http://www.nu.nl/internet/1306408/automatische-vertaling-leidt-tot-diplomatiek-incident.html