Capturing mobile phone traffic on Wireshark
Another option which has not been suggested here is to run the app you want to monitor in the Android emulator from the Android SDK. You can then easily capture the traffic with wireshark on the same machine.
This was the easiest option for me.
In addition to rupello's excellent answer, a "dirty" but very effective trick:
For all phones, any (local) network: Set up your PC to Man-In-The-Middle your mobile device.
Use Ettercap to do ARP spoofing between your mobile device and your router, and all your mobile's traffic will appear in Wireshark. See this tutorial for set-up details
Here are some suggestions:
For Android phones, any network: Root your phone, then install tcpdump on it. This app is a tcpdump wrapper that will install tcpdump and enable you to start captures using a GUI. Tip: You will need to make sure you supply the right interface name for the capture and this varies from one device to another, eg -i eth0 or -i tiwlan0 - or use -i any to log all interfaces
For Android 4.0+ phones: Android PCAP from Kismet uses the USB OTG interface to support packet capture without requiring root. I haven't tried this app, and there are some restrictions on the type of devices supported (see their page)
For Android phones: tPacketCapture uses the Android VPN service to intercept packets and capture them. I have used this app successfully, but it also seems to affect the performance with large traffic volumes (eg video streaming)
For IOS 5+ devices, any network: iOS 5 added a remote virtual interface (RVI) facility that lets you use Mac OS X packet trace programs to capture traces from an iOS device. See here for more details
For all phones, wi-fi only: Set up your Mac or PC as a wireless access point, then run wireshark on the computer.
For all phones, wi-fi only: Get a capture device that can sniff wi-fi. This has the advantage of giving you 802.11x headers as well, but you may miss some of the packets
Capture using a VPN server: Its fairly easy to set-up your own VPN server using OpenVPN. You can then route your traffic through your server by setting up the mobile device as a VPN client and capture the traffic on the server end.