What are the technical differences between 1X and 3G on Verizon's network? My Android device (on Verizon) will sometimes display 3G in the status area, and sometimes display 1X.  What do these indicate, and what is the difference?
The Verizon network uses a technology called CDMA2000, or CDMA for short.  There are different types of CDMA2000 connections.  The first is 1x, or 1xRTT, which has a potential throughput of 153kbps, but will likely be lower depending on signal strength.  When '1X' is displayed in the status bar, this is the connection type your device has.  

CDMA2000 1xEV-DO, or EV-DO for short, uses multiplexing to increase throughput.  The Rev.A version of the EV-DO standard has a potential throughput of around 3.1Mbps.  This is the connection type when 3G is displayed in the status bar.

Verizon is in the process of rolling out a technology called LTE which the carrier will market as their 4G service.  This new technology will allow much higher throughput (estimated 12Mbps at launch with the specification capable of delivering rates as high as 50-100Mbps).