Is this a custom field you've created in Marketo? If so, navigate to Admin > Field Management and find the field in the right navigation. You can then click the field and under "Field Actions" > "Change Type". However you can only perform this function once all references to the field have been removed from smart lists, forms, smart campaigns, etc.
The only thing I'd add to this is that you open yourselves up to a lot of potential duplicates, misspellings and a whole variety of different industries being inputted - as people will always have a different stance on exactly what their industry is. It'd definitely be cleaner to keep this as a predefined pick-list if you can.
The 'old'/existing industries in these fields won't change, unless someone resubmits a form and overwrites with a new value.
Are you referring to a standard field in Marketo or a custom field? In case it is a standard field then Marketo does not give the option to edit the field type. In case it is a custom field, we would first need to remove this field from all the associated smart campaigns, lists etc. Once this is done then we can change the field type (Reference link - http://docs.marketo.com/display/public/DOCS/Change+the+Type+of+a+Marketo+Custom+Field).
How ever like Carly rightly mentioned, this would give rise to a lot of possible duplicates and other problems. The problem is further complicated in case you are using such a field in Salesforce and using it to Sync the values with Marketo. In which case the Marketo SFDC sync could possibly get effected and Normalizing these values could be required.
As a recommendation I would suggest that in addition to the values in the pick list, you can add another value called "other" and a section just below to mention the Industry details.