Preparing for the zombie apocalypse is silly of course, but there are lots of realistic scenarios that could interrupt the normal infrastructure. How well you should prepare and for what depends on where you live. For example, from what I have heard the north american power grid, like the Scandinavian is susceptible to solar flares events. It's quite possible a flare will knock out the grid and damage transformers that could take several weeks to replace or repair (and maybe longer if much of the globe is affected). And then there are natural disasters, epidemics and of course war.
A lot of 'prepper' stuff you see on TV is just dumb though. I saw one couple who was hoarding liquor in their basement, they were God fearing people that didn't drink but for some reason they believed that ethanol would be super valuable after the apocalypse.
Having a bag with spare clothes and medicine and perhaps some food in case you need to evacuate from your home suddenly is probably a good idea though, and something many governments recommend. It's also a good idea to have food, medicine and some way to stay warm and cook at home in case of an extended blackout. I know in Sweden the government expect citizens to manage for at least 3 days without running water, electricity, medicines or food supplies. I suspect you need more than that because the government planing won't work perfectly since they've never tested their plans in real life. But exactly what you should keep and for how long depends on where you live and what your personal needs are.
Some things you can't really prepare for though. From what I've read you are lucky if you get wiped out by the initial strike during a nuclear war for example, so no need to worry about EMP's or fallout shelters! A lot of people are really naive, thinking they will be able to live of the land and so on, but you can tell they have never caught a fish in their life much less a rabbit. And they will have to compete with millions of other starving desperate people. A really bad pandemic could also be nasty but also something that is hard to prepare for. A bug out bag wouldn't help at all in those scenarios.
A bug out bag should only have the bare minimum you need to evacuate from your home quickly. If you have any tools at all I would say a pocket knife. A multimeter would be pretty low priority. Anyone who's been hiking in real life knows every gram you have to carry is 'expensive' (slow you down) so you only bring what is absolutely essential for the trip. I suspect people who have never hiked in their life will not get very far if they have to suddenly pack a bag and walk several miles during a disaster. So stay fit and go hiking is probably the first thing anyone who want to prepare for situations like that should do.