A conversation on a Vonage line is actually more secure than one over an ordinary phone line. A VoIP conversation is broken up into pieces called packets. These packets are sent over the Internet and reassembled at the listener's end. Packets contain no meaningful identifiers in them. Your account information, for example, is not transmitted in these packets. The packets don't necessarily take the same path over the Internet, and will travel only to the intended location (the listener). This means that someone can't simply tap into your conversation, or redirect your packets somewhere else.
Additionally, our servers that handle calls have various security features to prevent unauthorized access to the internal network. All of this makes Vonage an extremely secure means of communication.