I agree with Stanislav Sinyagin on the cloud based solutions, but I would add one more, Voxeo Prophecy. Tropo is from Voxeo, but they have offered Prophecy as a solution for a lot longer and it supports the open standards CCXML and VoiceXML. The advantage of CCXML for outbound notification applications is you have a lot more control of the notification process.
The Prophecy platform has excellent call progress analysis (CPA) which will allow you to determine whether a machine or a human answered and handle the call accordingly. For example, it does not make sense to ask a machine to "...press one to confirm". Instead you may want to leave a message that provides a call back number for the user to confirm with after they have listened to the voice message. The CPA can be used to leave a message on a machine at the correct time (when the greeting message has stopped) so that you do not get clipped messages in the voice mail. CPA will also allow you to provide detailed reports on who was notified and for those that did not it can tell you whether it was a bad number (received a SIT tone), a modem or fax answered, or ring-no-answer (pretty rare these days). These type of details can factor into your retry process for failed notifications.
The other advantage to using Prophecy and open standards is your application will be portable to other IVR systems that are VoiceXML/CCXML compatible if you ever want to migrate. Tropo, Twilio, and Plivo all use proprietary API's which does not allow you to move your applications to other services. Prophecy is also available as a software solution so that if you want to take it out of the cloud you can run it on premise. You can get a two port version for free to try it out.
There is excellent documentation on developing outbound notification systems on Voxeo's developer site. Take a look at the CCXML documentation in section F on Outbound Dialing.
Not sure which development languages you are familiar with, but if you are used to ASP.NET MVC there is an open source project called VoiceModel that makes it easier to develop VoiceXML applications. The other advantage of VoiceModel is that you develop your application once and it will run on any VoiceXML compatible platform and Tropo. They are currently working on adding outbound notification support in this project that will work for both Tropo and VoiceXML.