Scott has given a very comprehensive reply that just about covers all the major points. I'll just add my two cents worth....
I also use both analog and digital meters. I use digital for sensitive circuitry where high accuracy is important, but I still prefer analog for many day-to-day tasks.
As Scott mentioned, for house electrical work the high-impedance of a digital meter can give rise to some confusing readings, such as getting perhaps a 50 or 60V reading on a wire which is actually disconnected. (Without getting into the technical bits too much, this often happens where the wire runs a long distance with other wires which are hot.)
The clamp-on jaws won't work if you just put them around, say, an appliance cord, because at any given moment the currents in the hot and neutral are flowing in opposite directions and cancel out - It has to go around just one wire.
If you measure appliance current regularly, you can get a neat little adapter which connects between the plug and wall receptacle. This takes one side of the circuit straight through but brings the other into a plastic former around which you can clamp the jaws easily. Many have a second "x 10" section for measuring low currents.
I have one of these gizmos as an accessory to my Simpson 260.
