Can you give an example of an actual case when you needed this sudden burst of computational power? I'm curious what sorts of things people are actually using it for in real life. (instead of "well, you COULD use it for ....")

I use high-capacity EC2 for problem sets in my bioalgorithms class. Basically whenever something's taking too long for my liking on whatever machine I'm running it on, I'll throw it up on a beefy EC2 instance and let it run there.

Image processing and analysis (some of my work involves cbir), processing large amounts of data of statistical analysis, brute forcing needs, etc

Load simulations for VR systems

It's also good for hosting websites (well, duh) and especially excels when you need a lot of storage; EBS volumes are almost unbeatable on price and comfort.

I used it a lot for video encoding