Below are a few images collected via Google Earth of significant elevation gains.
In North America two of the most significant slopes Mt McKinley in Alaska and Mt St Elias on the Alaska-Yukon border. For the former, the base-to-peak rise is something like 5500m while the latter is one of the closest big mountains to the ocean.
The remaining images are from Asia. For sheer rise it’s hard to go past Nanga Parbat in Pakistan. The following shows a gain of close to 7000 metres.
The south-eastern slope of this mountain (Rupal face) has been called “the largest mountain face in the world”  rising some 4.5km in just 7km of horizontal distance!
Finally we turn to the mighty Himalayas. There are numerous large elevation gains here – among the most notable are the area among the peaks of Dhaulagiri, Annapurna I and Machhapuchhare. The Kali Gandaki River flows through this region.
Here is a world map of the mountains mentioned in this post.
Two oceanic rises that I could not gather images for are:
- Mauna Kea in the biggest island of Hawaii, which has the largest elevation gain anywhere on earth from the ocean floor – 10,200m, though this is over a distance of more than 100km.
- From Challenger Deep, the deepest point in the ocean, to a point about 65km north west there is a rise of some 9500m from 11900m below sea level to 2400m below sea level.
 World Top 25 by Reduced ORS – http://www.peaklist.org/spire/lists/world-top-25-angle.html
 summitpost.org discussion thread: Great Elevation Gains : General – http://www.summitpost.org/phpBB3/great-elevation-gains-t57242.html