If I buy an app in the App Store, will it work on future major releases or will I need to repurchase it?
Yes it is definitively possible. As of now, Apple does not enable the developers to publish paid updates for their software. Due to that, developers sometimes release different versions to buy from the App Store.

E.g. have a look at http://itunes.apple.com/de/app/photoforge/id314173066 and http://itunes.apple.com/de/app/photoforge2/id435789422