Jmurray...if your ranger had been given a 3-core flex, it wouldn't make it dangerous -as such. Fact is, anything which has exposed metalwork that has been earthed runs the risk of becoming live if the earth wire is accidently connected to the live terminal in the plug, or more likely if the wires have been connected wrong inside the appliance. The chances of any of that happening are slim, but I have known it happen. As have I known 13amp wall fittings being wired up wrong, with the live wire being placed in the earth terminal on either a wall socket or switched / fused plate controlling it. The potential is there.
Now, that is all down to human error, and the likelihood of that sort of thing happening has to be weighed up against the chances of the appliance becoming faulty, and as a result live connections coming into contact with exposed metal work. In the case of an earthed appliance, it will have been considered more likely that the outer casing could become live through a fault, than ever it might through human error. You could say in an ideal world that no appliance would need an earth wire if it could be made in a way that metal work could never become live. That is the basis of a double insulated [none-earthed] appliance; they are designed in such a way that the exposed metal parts should never come into contact with a roaming live connection, if all the original factory-fitted flex guides, hooks, and sleeves etc. are in place. Next time you take your ranger to bits, have a look at it slowly and note the way all the wires are a certain length, and have plastic sleeves on the terminals, and are anchored down to prevent movement, should a wire come loose.
For some reason, a lot of DIYers use 3-core flex to replace 2-core on appliances. Mostly they will cut the earth wire out at the appliance end, but still connect it at the plug end, which I suppose is the best of a bad job, as at least if the earth wire was to touch anything live, it would be earthed at the other end. However, I have seen many an occasion where someone attached the earth wire to the body of the cleaner. I guess the culprit thought they knew better than the manufacturer. Given that the cleaner will have been insulated thoroughly (as I explained earlier), this is not neccesary and as before, in very rare cases could introduce a danger where none would ever exist if it was left alone.
Appliances with water will often have an earth wire as a leak of water can carry electricity if it is in contact with a live part, but then you know this. Although I can never get my head around it, Hoover wet & dry cleaners from the late 80's onwards never had earth connections, nor did later Vax cleaners. Also in the mid 1980's Tefal did a table-top washing machine and matching spinner, neither of which were earthed.
You will have to go a long way to find a modern vacuum cleaner which is earthed. In recent years I have seen a Vax and Electrolux commercial uprights with earth wires, and Kirby always used to be earthed, but it has been a number of years since I last fixed any vacuum cleaner, let alone a Kirby.
Now to contradict myself, having suggested throughout that the manufacturers know best, they may do about earthing, but I often disagree with their choice of flex and plugs attached to many new appliances. I have recently seen a cheap fan heater fitted with 0.75mm flex. The appliance runs at 2KW, but such is the shortage of copper, and the cost so high, all appliances now have leads much thinner than I would think safe. I first noticed it with kettles, but there is the usage time to be taken into account there, where a kettle will normally only be used for a minute or two. This means that the flex is providing power for only a short time. In the case of a fan heater, it will be running at full power for as long as the thermostat allows. I do not like it one bit. 13amp plugs are now appalling. The moulded plugs have always ranged from OK to perfect, but in the last 15 years or thereabouts, the spectrum for moulded plugs has increased dramatically. Some are terrible. As are a lot of modern extention leads, but that's another debate.