Is there a mobile phone which offers the option to send a text to your whole phone book?

It depends on your cell carrier. I have the new HTC Evo from Sprint allows you to do that + more. Depending on some phones you get as well as the plan you have, won't allow you to, but most phones allow you to do that. All you should be able to do is go to like your sending a text message, type your message or add your contacts, and send. it should work. Depending on the phone you have, you may have to keep sending the message to your contacts depending on how many it allows you to send a time.. Hope that helps.

I know that AT&T and T-mobile don't allow this.