I had downloaded some music from Internet using Ubuntu 6.06. However, when I booted into Windows XP Professional, it cannot read the partition from Ubuntu. Neither can I read or even see the files I created in Linux even I saved in the Windows Parition. (It is like I mounted the Windows parition in /windows/personal and I downloaded music into /windows/personal using Ubuntu)
What should I do other than send these files into my email and re-download them into my Windows.

The default method of mounting FAT32/NTFS partitions in Linux is as read-only so You can't write on them from within Ubuntu. But You would most certainly have noticed if this the problem, ie You can't save files to the Windows partition.

To be able to read a Linux partition (ext3 or other filesystem) from within Windows You must have a program that can read and copy files from it. I have used explore2fs-1.08beta9.exe with some success. Google for it.

There are few ways to easily work with files over OS/file system boundaries. One could be to have a DATA partition formatted with FAT32 that is available from both OSs. Or mount NTFS with write enabled. I'm not sure, but I still think it is not recommended.

I second, you should mount the ntfs with write access, this is a topic that has been well covered for ubuntu, I would go to the ubuntu community docs and seach for it there. Windows could never read disks or files from other operating systems (even though other operating systems generally all can read windows files and disks).