Tools

Below are some of the Tools, Software and Apps I like to use.  Item with a "*" at the end of the description are licensed under GNU or similar Freeware licensing, please check before use.

Packet Inspection
WireShark (O,W) - In my opinion, this is hands down the best network protocol analyzer. You can capture and interactively browse the traffic running on a computer network.  You can view all PDU info (size, header info and contents, and even save captures for later analysis.  It supports sorting, filtering, search.  I have used this several times to track down the source of network problems and as a training tool in my network class.  The website has some great how-to videos to help you learn how to use it, and there is even a portable version. *

Productivity Software
FreeOCR (W) - OCR Software. *

Remote Desktop
PocketCloud (A,I) - Supports Microsoft RDP, VNC and VMWare View 4.5 protocols.*, $14.99 

WLAN
Ekahau HeatMapper (W) - Wi-Fi Coverage Map Site Survey Tool *
inSIDDer (L,W) - Wi-Fi scanner, it tracks signal strength over time, identifies security settings, supports filtering and can be GPS aware. *
Network Info II (A) - All of your radio info in one place, it displays info about the phone and current data network, Bluetooth, IPv6 and Cell connection. *
WiFi Analyzer (A) - Basic Wi-Fi radio frequency analyzer. This is the first tool I use to look for networks and Wi-Fi problems. *
WiFiFoFum (A,I) - WiFi network scanner, displays information about SSID, MAC, RSSI, channel, security and is GPS aware. *, $2.99

More to come!

OS Reference
A - Android
I - iOS
L - Linux
O - OSX
W - Windows