It depends on what the device is, but yes, an 'alive' LED, or pulsing LED can be very helpful. The methods MisterT stated are also very good. The more indicators, the more information you can convey; e.g. indicators for Tx/rx, packet received, error, etc. can all be useful to tell you the state of the device both during development and when it's deployed.
I also have used debug messages (software enabled) sent out the communications port, interspersed with the real data packets; you can obviously get more information from a serial message than you can from a flashing LED or two.