楼主你描述的不是很具体，也不知道是linux系统还是win系统，不知道要备份系统自带的驱动还是安装其他程序时附加的驱动。
如果你是linux系统可是尝试一下使用unixODBC，编译安装的教程网上有的是。备份一些特定数据库的ODBC驱动的话只需要备份两个对应的so文件，在使用ODBCmanger工具导入即可。

如果是win系统的话可能稍微复杂些。以系统自带的ODBC驱动为例，可以首先在Windows/system32文件夹中查找odbcconf.rsp，用记事本查看有类似下边的内容
INSTALLDRVRMGR
INSTALLTRANSLATOR "MS Code Page Translator|Translator=MSCPXL32.dll||"
INSTALLDRIVER "SQL Server|Driver=SQLSRV32.dll|Setup=sqlsrv32.dll|SQLLevel=1|FileUsage=0|DriverODBCVer=03.50|ConnectFunctions=YYY|APILevel=2|CPTimeout=60||"
INSTALLDRIVER "Microsoft ODBC for Oracle|Driver=msorcl32.dll|Setup=msorcl32.dll|SQLLevel=1|FileUsage=0|DriverODBCVer=02.50|ConnectFunctions=YYY|APILevel=1|CPTimeout=120||"
INSTALLDRIVER "Microsoft Access Driver (*.mdb)|Driver=odbcjt32.dll|Setup=odbcjt32.dll|APILevel=1|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=2|FileExtns=*.mdb|SQLLevel=0||"
INSTALLDRIVER "Microsoft Text Driver (*.txt; *.csv)|Driver=odbcjt32.dll|Setup=odtext32.dll|APILevel=1|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.,*.asc,*.csv,*.tab,*.txt,*.csv|SQLLevel=0||"
INSTALLDRIVER "Microsoft Excel Driver (*.xls)|Driver=odbcjt32.dll|Setup=odexl32.dll|APILevel=1|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.xls|SQLLevel=0||"
INSTALLDRIVER "Microsoft dBase Driver (*.dbf)|Driver=odbcjt32.dll|Setup=oddbse32.dll|APILevel=1|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.dbf,*.ndx,*.mdx|SQLLevel=0||"
INSTALLDRIVER "Microsoft Paradox Driver (*.db )|Driver=odbcjt32.dll|Setup=odpdx32.dll|APILevel=1|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.db|SQLLevel=0||"
INSTALLDRIVER "Microsoft Visual FoxPro Driver|Driver=vfpodbc.dll|Setup=vfpodbc.dll|APILevel=0|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.dbf,*.cdx,*.idx,*.fpt|SQLLevel=0||"
INSTALLDRIVER "Microsoft FoxPro VFP Driver (*.dbf)|Driver=vfpodbc.dll|Setup=vfpodbc.dll|APILevel=0|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.dbf,*.cdx,*.idx,*.fpt|SQLLevel=0||"
INSTALLDRIVER "Microsoft dBase VFP Driver (*.dbf)|Driver=vfpodbc.dll|Setup=vfpodbc.dll|APILevel=0|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.dbf,*.cdx,*.idx,*.fpt|SQLLevel=0||"

INSTALLTRANSLATOR "MS Code Page-躡ersetzer|Translator=MSCPXL32.dll||"
INSTALLDRIVER "Microsoft Access-Treiber (*.mdb)|Driver=odbcjt32.dll|Setup=odbcjt32.dll|APILevel=1|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=2|FileExtns=*.mdb|SQLLevel=0||"
INSTALLDRIVER "Microsoft Text-Treiber (*.txt; *.csv)|Driver=odbcjt32.dll|Setup=odtext32.dll|APILevel=1|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.,*.asc,*.csv,*.tab,*.txt,*.csv|SQLLevel=0||"
INSTALLDRIVER "Microsoft Excel-Treiber (*.xls)|Driver=odbcjt32.dll|Setup=odexl32.dll|APILevel=1|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.xls|SQLLevel=0||"
INSTALLDRIVER "Microsoft dBase-Treiber (*.dbf)|Driver=odbcjt32.dll|Setup=oddbse32.dll|APILevel=1|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.dbf,*.ndx,*.mdx|SQLLevel=0||"
INSTALLDRIVER "Microsoft Paradox-Treiber (*.db )|Driver=odbcjt32.dll|Setup=odpdx32.dll|APILevel=1|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.db|SQLLevel=0||"
INSTALLDRIVER "Microsoft Visual FoxPro-Treiber|Driver=vfpodbc.dll|Setup=vfpodbc.dll|APILevel=0|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.dbf,*.cdx,*.idx,*.fpt|SQLLevel=0||"

INSTALLTRANSLATOR "Conversor de p醙ina de c骴igo MS|Translator=MSCPXL32.dll||"
INSTALLDRIVER "Driver do Microsoft Access (*.mdb)|Driver=odbcjt32.dll|Setup=odbcjt32.dll|APILevel=1|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=2|FileExtns=*.mdb|SQLLevel=0||"
INSTALLDRIVER "Driver da Microsoft para arquivos texto (*.txt; *.csv)|Driver=odbcjt32.dll|Setup=odtext32.dll|APILevel=1|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.,*.asc,*.csv,*.tab,*.txt,*.csv|SQLLevel=0||"
INSTALLDRIVER "Driver do Microsoft Excel(*.xls)|Driver=odbcjt32.dll|Setup=odexl32.dll|APILevel=1|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.xls|SQLLevel=0||"
INSTALLDRIVER "Driver do Microsoft dBase (*.dbf)|Driver=odbcjt32.dll|Setup=oddbse32.dll|APILevel=1|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.dbf,*.ndx,*.mdx|SQLLevel=0||"
INSTALLDRIVER "Driver do Microsoft Paradox (*.db )|Driver=odbcjt32.dll|Setup=odpdx32.dll|APILevel=1|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.db|SQLLevel=0||"
INSTALLDRIVER "Driver para o Microsoft Visual FoxPro|Driver=vfpodbc.dll|Setup=vfpodbc.dll|APILevel=0|ConnectFunctions=YYN|DriverODBCVer=02.50|FileUsage=1|FileExtns=*.dbf,*.cdx,*.idx,*.fpt|SQLLevel=0||"

SETFILEDSNDIR

可以找到Driver和Setup所对应的dll文件进行备份就可以了。

在恢复的时候，把这些文件放在windows/system32文件夹下，并在cmd中执行：

odbcconf.exe /S /Lv odbcconf.log /F %systemroot%\system32\odbcconf.rsp

如果备份特定的数据库的ODBC驱动，方法与此类似，不做赘述了~
由于也不太清楚你的具体情况，在这里就根据经验写出这些，希望对你有所帮助。

是windows   xp谢谢楼上的，我在研究，你的回答给我的帮助很大，O(∩_∩)O谢谢