Often when bored in meetings, would like to turn my phone off so calls go right to voice mail but still be able to check email/internet browse. Couldn't do it with my windows phone, wondering if at all possible on android
You can turn on call forwarding and send the call to another number or directly to voicemail.
Why not just silent your phone? Won't ring and you still have access to your email and browser. I do this all the time.