FME Licensing Details

FME requires a licensed ArcGIS installation to support Geodatabase formats:

Personal Geodatabase (File and MDB)
  • Reading: ArcView or ArcEngine level or higher
  • Writing: ArcView or ArcEngine level or higher

SDE Geodatabase
  • Reading: ArcView or ArcEngine level or higher
  • Writing: ArcEditor or ArcEngine with the Geodatabase Update Extension

From the Esri ArcEngine FAQ page comes the additional information that an ArcEngine license cannot be deployed on a Server machine.

http://www.esri.com/software/arcgis/arcgisengine/common-questions.html

Esri ArcGIS Licensing

In addition, in the ArcGIS 10 help here, can be found what geodatabase functionality is available at the various Esri ArcGIS license levels.