I formatted my USB drive in Ubuntu's disk utility. When I plug that USB into my PC which has Windows XP on it, it shows the drive as corrupted.
That same USB works on Windows 7 and 8, just not with Windows XP. How can this be fixed?
There are actually differences between NTFS used in different Windows versions, as described in this Wikipedia page.
For the most part, you can use NTFS volumes in a dual-boot system under XP and Windows 7, but there can be some issues with some of the more esoteric stuff. For example, XP can only deal with one System Restore point. If you mount a Windows 7 or Vista volume with multiple restore points, XP sees them as invalid and deletes all of them. Therefore you should avoid using an NTFS volume with XP if you are depending on restoring to a previous version.
To be more precise: Windows XP, Vista and 7 all use NTFS version 3.1. However, NTFS 3.1 is a highly complex and advanced file system, and in fact its design includes features that not all versions of Windows can support. So, there is no chance of Windows XP corrupting a Windows 7 volume (making all data impossible to access), however XP may destroy data that Windows 7 saved to disk, if said data is 7-specific.