Moving data in multiple tables from old database to one table in new database
You can use SSIS (from sql 2005 and up)to transfer data from one database.Table to anotherDatabase.Table or all tables as well.

Note: SQL Server Import and Export Wizard will give you option to save the package at the end so that you can reuse the package for subsequent data transfer.

You need to be careful with constraints on the destination database. You can temporarily disable them and then reenable then once your data load is done. Script by Aaron can be found at Temporarily disable all foreign key constraints

If the tables from source and destination have exactly same schema, then you can use bcp as well. for script refer to my answer here.