Wireshark - Wireshark is a network protocol analyzer for Unix and Windows. It lets you capture and interactively browse the traffic running on a computer network.
NetMonster - NetMonster is a networking app by Michal Mrocek that comes up with features to enable you to get detailed information about your current network right on your mobile phone screen.
tcpdump - tcpdump is a common packet analyzer that runs under the command line.
Mojo Packets - Wireless Troubleshooting Made Easy
PCAPdroid - PCAPdroid is an android app to capture the phone traffic and analyze it remotely (e.g. via Wireshark). The traffic can be easily downloaded from a remote device thanks to the integrated HTTP server, or streamed to a remote UDP receiver.
NetMonitor Cell Signal Logging - NetMonitor Cell Signal Logging app helps you in receiving accurate measurements of the speed of the internet and the strength of signals to choose the correct network according to your needs.