Here are couple things you can do and all of these have advantages and disadvantages:
Manual scripting and linked servers:
Setup linked server connections and use INSERT INTO
INSERT INTO server2008.databaseName.schemaName.TableName (Col1, Col2, ..., Coln)
SELECT Col1, Col2, ..., Coln
FROM server2000.databaseName.schemaName.TableName
Mind the execution order of these. Make sure to first migrate tables that have no references to avoid issues with foreign keys
You can even temporary disable foreign keys and identity inserts on some tables
ALTER TABLE MyTable NOCHECK CONSTRAINT FK_Constraint
SET IDENTITY_INSERT tableName ON
-- INSERT STATEMENT HERE
SET IDENTITY_INSERT tableName OFF
ALTER TABLE MyTable CHECK CONSTRAINT FK_Constraint
Export Data Wizard
Already suggested by Tomasito – just make sure to execute scripts in correct order. First scripts for tables with no references , than tables that only reference data in previously inserted tables and so on….
Third party tools
There are many of these that will do the job for you. If this is a one-time task you can get the job done using trial version. Couple I know are ApexSQL Data Diff, SQL Data Compare, AdeptSQL Diff.