Interception:
Typically, the encryption of voice communications (and of text messages) that travel through the mobile phone network is relatively weak. There are inexpensive techniques which third parties can use to intercept your written communications, or listen to your calls, if they are in proximity to the phone and can receive transmissions from it. Of course, mobile phone providers have access to all your voice and text communications.
It is currently expensive and/or somewhat technically cumbersome to encrypt phone calls so that even the mobile phone provider can't eavesdrop – however, these tools are expected to become cheaper soon. To deploy the encryption you would first have to install an encryption application on your phone, as well as on the device of the person with whom you plan to communicate with. Then you would use this application to send and receive encrypted calls and/or messages. Encryption software is currently only supported on a few models of so-called 'smart' phones.
Eavesdropping:
Your phone can be set to record and transmit any sounds within the range of its microphone without your knowledge. Some phones can be switched on remotely and brought into action in this way - even when they look as though they are switched off. Never let people you don't trust have physical access to your phone; this is a common way of installing spying software on your phone. If you are conducting private and important meetings, switch your phone off and disconnect the battery. If possible do not carry the phone with you, leave it somewhere where it will be absolutely safe. Make sure that any person with whom you communicate with also employs the safety measures described here.
In addition, do not forget that using a phone in public, or in places that you don't trust, makes you vulnerable to traditional eavesdropping techniques, or to having your phone stolen.