In Access, when entering a value "directly" into a table (either in Datasheet View or in a bound form), simply leaving the cell/control empty will attempt to insert a NULL value. If the corresponding column in the underlying table does not allow NULL values then the insert will fail.
The workaround for that is to type
""
into the cell/control to specify an empty string (which is not the same as a NULL value). I just tested this on an ODBC linked table against SQL Server 2008 R2 from Access 2010 and it worked.