When purchasing software, how many releases of Ubuntu will that software be available to me?
As in the title, if I purchase software and install the next version of Ubuntu will I have to purchase it again?
No. It is linked to your Ubuntu One account.
This is apart from the fact that you don't have to reinstall Ubuntu when the next version is released: you just let Update Manager perform the upgrade for you!
As Jonathon says: it's linked to your UbuntuOne account.
I don't know if you get newer versions though (in case that would be required for a newer Ubuntu version).