I can see a point if you live in a place where there are tornados passing by now and then, but then you gould have a HUGE backpack or hockey trunk filled with goodies like a good sleeping bag etc. It should not be too big though, if you have to travel by bus.
If you are living in a populated area and have to leave your house (like if the neighbouring chem plant is on fire) you will most likely be accomodated indoors by whatever agency is responsible for that. If so you dont need axes and guns and such, but more civilised stuff, like games for kids, medicines you need and other more regular everyday items. If you are evacuated from A to B because of a fire, the society outside the fire still works and you wont end up in a hole in the ground. If there is a tornado or civil war going on, you might end up in the hole in the ground and need to accessorise accordingly.
I checked the Swedish civil defence site
www.civil.se for info and since there is no threat for eminent war (since the Russians are friendly again

) there is just info on how to "survive" a power out.
http://www.civil.se/rad_burken.pbs You can see fotr yourself, the white things are spare plugs. They also advice that water cleaninig tablets are not available anymore but can be substituted with a coffee filter, and you can heat water in a ginger bread box for an hour or so. Strange advice.
Anyway, unless there is a civil war, a fireworks factory exploding or the third biggest oil depot going up in flames, there is rarely need for a bug out bag in a normal home. In a boat its a different thing, but then you need other types of stuff. Would a water tight box with floating stuff on it be a bad idea, just toss it overboard if you have to leave.