Short Answer:

There is no limit. 

Long Answer:

An External ID has two parts:  module and name, separated by a period character during import. 

Each part can have up to 10,485,760 characters.

The total length of an External ID is 20,971,520 characters - 10,485,760 each side of the "." in the middle.

An example of a "long" External ID in Odoo is:

account_reports.selection__account_financial_html_report_line__special_date_changer__to_beginning_of_period

You will run into a practical limit of working with External ID's in technology (user experience issues - editing/display) well before you run into physical limitations or performance issues.