Just put a current transformer on the incoming cable and connect it to the line in of your computer with a small resistor across it to convert the signal into a voltage. Connect another current transformer to a meter so that you can calibrate the card.
Run an oscilloscope application so that you can check to make sure that you aren't overdriving the input, adjust the value of the resistor down if necessary.
Now you need a simple program to periodically sample and calculate the rms current. Save the samples to a log file. I do this using an Efergy wireless monitor that came with three current transformers but since I only have a single phase supply I only needed one so I used one of the spares and a program written in VB6 on an old Win98SE machine to monitor the current.
To get good accuracy you will need to do some careful calibration but it seems to be pretty stable. Actually the newer Efergy monitors come with a computer hardware interface of some kind and software.
if you want to do this in *nix there are plenty of programs and libraries for reading from the sound card and then you can use all sorts of techniques including shell scripting to analyse the results, sound alarms, etc.