Most mobile operators will allow you to block SMS (text messages) to your phone. You need to call your operator to find out what service they offer to do so. Verizon Wireless, for example, allows you to block up to five phone numbers. You can do this through your account online or by calling your operator. T-Mobile and Vodafone UK, on the other hand, only allow you to block all text messages, not those from specific mobile numbers.