Amazon do negotiate individual prices in some circumstances.
I'm not entirely sure what circumstances it takes to make them negotiate, but the discounts I've heard about are significant. It doesn't seem to be based on the size of the deal though.
The only times I've heard of this were GovCloud (which costs more, but includes a lot of extra service) and the recent announcement of volume based pricing (which is sort of individual in a way).
Dropbox, Heroku, and Netflix would be the authoritative data points, I think. I've heard "won't do anything custom", but I never really pushed to find out about discounts. Even if they do exist, they're nowhere near as common as with every other provider (where either you get a marketing deal discount, or can just get a discount for the asking, especially early on, or as you grow).
I'm not entirely sure what circumstances it takes to make them negotiate, but the discounts I've heard about are significant. It doesn't seem to be based on the size of the deal though.