In theory, it can be rather large. From ESRI documentation it appears that it could be as much as 256 Terabytes using the appropiate configuration keyword.
But as for the reality, hard to say.
The Top 9 Reasons to Use a File Geodatabase - ESRI (PDF)
Chris Donohue, GISP
Thanks for the info Chris. Since I posed the question I've done a bit more searching and came up with this from "Building Geodatabases Course Q&A by Rudy Prosser:
Q: What’s the size of the BLOB in a file geodatabase (used to store attachments)?
A: Field size information is documented in ArcGIS Help at several locations. If you’re using an RDBMS to store your geodatabase, see DBMS data types supported by ArcGIS. If you’re using a file geodatabase, see File geodatabase size and name limits. For information on supported field types, see ArcGIS field data types. As best as I can determine, the maximum BLOB size is 2 GB.
Also, ESRI 10.2 help had this about file Geodatabases:
File geodatabase size and name limits
File geodatabase size and name limits are as follows:
File geodatabase size: No limit
Table or feature class size: 1 TB (default), 4 GB or 256 TB with keyword
Number of feature classes and tables: 2,147,483,647
Number of fields in a feature class or table: 65,534
Number of rows in a feature class or table: 2,147,483,647
Geodatabase name length: Number of characters the operating system allows in a folder name
Feature class or table name length: 160 characters
Field name length: 64 characters
Text field width: 2,147,483,647
Seems like the 2Gb is a recurring theme so I feel comfortable in agreeing with Rudy's assessment.
Hopefully this will help others as well.