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.
Charles Proxy - HTTP proxy / HTTP monitor / Reverse Proxy
tcpdump - tcpdump is a common packet analyzer that runs under the command line.
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.
Postman - The Collaboration Platform for API Development
Mojo Packets - Wireless Troubleshooting Made Easy