One thing that I didn't realize I loved about sprints until I went to a place without them is the guarantee what for the next two weeks, your priorities are set, and aren't changing unless something very unexpected happens.

Having a two week period with a decided set of work allows you to peacefully do this work isolated from incoming requests - unless they are critical, they will always be delayed to the next sprint. Without sprints, our direction and priority changed daily, with no ability to say "we haven't planned for this, please wait". The result was it was incredibly hard to get anything done, and attention was always scattered.

I am happily back at a place that is doing sprints, and I am sure the problems at my previous organization were far bigger than not having them, but sprints do seem like a great tool to isolate the developer from exterior fluctuations. Granted, a great project manager can probably do the same thing.