When using ODBC targets you will need to make sure that:
The System DSN referenced in the ODBC target is present on all computers writing to the database. This requirement does not apply to version 2.50 (and higher) which also supports connection strings. Otherwise, you can use AutoAdministrator to push out DSN names to remote machines.
When using Microsoft Access, make sure that the System DSN (or connection string) are pointing to the database using an UNC path (e.g. \server\accesshare\EventSentry.mdb) and not a mapped drive letter.
The database ODBC drivers for the database you are using are installed on the remote computers. Windows 2000 and higher include the MS SQL and MS Access drivers by default, all other drivers (e.g. MySQL) will need to be installed manually.