The only recommended way to upgrade default applications provided with Ubuntu is through backports. To enable the backports repository, follow these steps:
- Open 'Ubuntu Software Centre'
- Click on the 'Edit' menu item, then 'Software Sources'.
- Enter your password if prompted.
- In the dialog that has just opened, click on the tab labelled 'Updates'.
- Tick the item labelled 'Unsupported updates (maverick-backports)', and click 'Close'.
Once you've done this, new unsupported major updates will be provided along with the usual security and recommended updates in Update Manager.
If the backports repository doesn't provide the new versions of software you want, you can search online for PPAs. Bear in mind that PPAs are usually intended for testing purposes only.
Supporting new applications with new system requirements and package dependencies is very difficult without upgrading the system itself. This is why Ubuntu has chosen to only release new major versions of software when the underlying system has been tested and upgraded.
For more details about PPAs, see this question:
What are PPAs and how do I use them?