It's certainly possible with Nexmo - as the other answer and comment state, it's not possible with Twilio & Tropo. Plivo's docs look like their delivery receipts are similar to Nexmo's.
Nexmo sends a delivery receipt if it's supported by the carrier. In the US it's not, but internationally it is supported often. In those cases Nexmo will give your app a callback with a delivery receipt. You can also use the message ID to query for the message status.
This screencast shows checking the DLR from the dashboard, which is really just a UI on top of the API.
Kevin makes the point that this could be difficult if the message is bounced through multiple providers - one of Nexmo's focuses is getting as direct a connection as possible.
[Disclaimer: I do occasional developer evangelism for Nexmo.]