The only trouble with most cheaper inverters is that they don't tend to produce a "clean" sine-wave output - usually nearer a saw-tooth. Most laptop power supplies usually rectify (convert to DC) and smooth the output voltage, so this shouldn't really matter. I do reckon though that my laptop's mains power supply does seem to run hotter on an inverter than on the mains, so it might be putting more strain on the transformer and smoothing capacitor.

Harpgirl, most of the cheaper inverters over here in the UK seem to be rated at 150w. At full power this would be probably be drawing at least 13a from your car battery - it's about the same load as full main beams and emergency rear fog lamps turned on together. I would definitely suggest keeping your engine running. Incidently, I would expect even a small coffee pot to have greater power requirements than 150w. Heating devices tend to require quite a lot of power and 12v batteries are not the best source. There are small 12v drink heater available, but I'd still tend to keep the engine running if I was using one of these.

Finally, cigarette lighter style sockets are officially rated at 10a, and will usually be fused accordingly. If you do want to take heavier currents from one, not only do you need to fit a higher value fuse, you must also make sure that the supply cables to it from the battery can handle the increased current. When my boat was surveyed for it's safety certificate, the examiner, made me replace a 16a fuse with a 10a for that reason - even though my wiring could handle 18a.