Voicemail is a feature offered by many landline phone companies and automatically included with many cell phone packages. You can block, or keep callers from leaving messages on your voicemail. No service has selective blocking to keep certain callers from being able to leave a message, but you can temporarily or permanently block all callers from leaving messages on your voicemail. The simplest way is to leave your voicemail full so there is no space available for additional messages.
Forward all cellular or landline calls to another number without voicemail. Verizon Wireless users, for example, can enable call forwarding in their online Verizon Wireless account; AT&T home phone users can select "*72 or 72# or 1172" on their phone to enable call forwarding. Once enabled, the call will be immediately forwarded, and the voicemail connected to the original number will not be accessible.
Cancel voicemail service. Landline phones have optional voicemail service and this service can be cancelled so no one will be able to leave a voicemail message. To cancel, call customer service.
Disable or modify a mobile phone voicemail. Since voicemail is standard with mobile phones, disabling or modifying this feature will block the voicemail. The procedure varies per cellular service. For example, AT&T requires you call your voicemail, select "Personal Options" and then "Administrative Options." Then select to turn off "Cut Through Paging." Sprint also requires you dial your voicemail, select "Personal Options," then select to "Change the Greeting" and choose the option to "Disable the Instructions." Disabling the instructions will prevent a caller from being able to leave a voicemail.