One of the first services to offer hosted telecommunication services by exposing an API for developers to create telephony services was Ribbit - developer.ribbit.com. Ribbit offers a Flex SDK to develop telephony services.
It is interresting to see a lot of startups recently offering cloud based approach to telephony services with even simpler API's that give even the most telco-unexperienced developers the tools to create cool telephony services.
Examples of telco in the cloud services:
Create ivr servies in minutes without even any hardware.