The default, generic voicemail greeting that comes with your iPhone is fine but also rather bland and boring. You can personalize the voicemail greeting on iPhone by recording your own custom version of it. This is a tutorial on how to create a custom iPhone Voicemail greeting.
After setting the number on your voicemail, you must also record a personal voicemail greeting. Follow the steps below. Start the Phone app. if you don’t see the numeric keypad, tap “Keypad” at the bottom of the screen. Tap and hold the “1” for about two seconds until the phone automatically calls voicemail. Immediately tap “3” to access voicemail settings. Listen to the options. On most voicemail systems, tap “2” to start the process to record a new greeting. The current personal greeting will play; then tap “2” again to record a new greeting. Say the greeting you want, and tap “#” when you’re done. To save the greeting, tap “1.” The personal voicemail greeting has been set. Hangup the phone. How to setup voicemail using a Visual Voicemail Applications

source: I have had the same voicemail greeting for 6you years and would like to change it. how do i change my voicemail greeting on my droid x2? thanx?
Select Phone.Select Voicemail.Select Call Voicemail.Calling Voicemail. If your voicemail is calling like on this screen, your phone is set up correctly. If not, follow the next few steps.Select Keypad.Enter the Voicemail number and select Call. **004*#Select Dismiss.