My experience is it would be better to provision a cluster of EC2 boxes to run the task than build a purpose-built super computer (with some exception). One disadvantage of clustered machines is longer communication latency, so tasks that require lots of process to process communication will run slower. Many problems can be tweaked with search spaces sliced so that this latency is not a big deal.
There are huge classes of problems were you can't tweak things like this. Basically any simulation where things are large distances interact or where there is a lot of communication can't really be shoved into a cluster. For example, computation fluid dynamics (e.g. anything looking at air or water moving over surfaces), weather simulations, molecular dynamics, simulating gravity, etc. All of these types of problems will run like crap if you try to use EC2 instances for them.
Also, have you really priced out what computation and data storage on EC2 costs? There's a few studies that show that EC2 on-demand instance will cost you 2-3 times more than purchasing a comparable server even with power, cooling, and maintenance/administration factored in. See, this or this for example. EC2 is great if you want to explore certain problems and need to temporarily scale up or want the ability to scale up on demand but if you have a base level of work that you'll be doing all the time, it's much more efficient to buy your own hardware. That is doubly true if your problems need any significant amount of storage space.