Side-by-Side (with Dropbox Support)
Price: Free or $1.99 for Pro
Research on the iPad is often difficult to do because you are constantly flipping between web apps and note taking apps. This is where Side-by-Side can really help. It splits the screen to display a web browser on one side and a note taking app on the other to allow for easy copying and pasting and writing. In addition, Side-by-Side can also display documents and images in the split screens.
Side by Side app overview
These are just a few ideas. I'm sure you can come up with even more.
This app isn't the most awe inspiring but it is useful. The free version and the paid version are identical except for the ad that runs on the free version.