If you are using MapInfo Pro, you can very easily convert the tab files in to GML using the Universal Translator tool. For converting to a KML format we have the Google Earth utility which can export these tab files to KML extension files.
For converting the GML file to tab file:
Go to the HOME tab > Tools Extension > Double click on the Universal Translator tool to open the FME Quick Translator window
In the FME Quick Translator window > Click on File menu > Translate
In the Set Translation Parameter window
Reader Format : Choose the tab file
Dataset: Choose the path of the file to be converted
In the Writer Format: Choose the GML extension option
Dataset: choose the name of the file to save as
Click on OK.
The file gets converted and the message says : Translation was SUCCESSFUL ; Translation finished.