The most common reasons are trying to stuff too large a value into a field. For example, if you have a Field whose Datatype is set to Integer, and you try to stuff 2,345,567 into it you'll get that error.
Are you importing into an existing table? If not, it seems that Access uses the first 40 or so lines to determine what type of field to build when importing files into a table. If those first 40 or so lines all contain Integer values, for example, Access will add an Integer field. Subsequent data may cause your overflow error.
The solution is to pre-build your table, making sure that your fields are of sufficient size to handle your incoming data, or to pre-pend a "dummy" row to your text file to force Access to build the table correctly.
