Breathable air is probably the greatest and most common thing taken for granted. There are actually many airborne threats, or ways you can be deprived of breathable oxygen, or be exposed to toxins that can kill you, but thankfully most are unlikely. In the natural word, smoke is probably the most common, such as a forest fire, but smoke is usually hotter than the air around it and rises up and out of the way. Volcanic (and super volcanic, ie. Yellowstone) eruptions is one of the bigger threats, releasing some toxic gases, but mainly ash, pumas, which are usually very tiny, sharp, and porous. It will choke engines of all types, and you will have to filter the air so you can breathe or it will basically turn to cement in your lungs. Similar conditions can be caused by an asteroid (meteorite) or comet impact – this will be presumably less uniform and contain stuff from whatever is thrown up where the impact took place, to the material of the meteorite itself.
Besides fires, man made threats come in three main categories, nuclear, chemical and biological. Nuclear ground bursts – which create huge amounts a radio active materials, are similar to the volcanic and asteroid impact scenarios with the addition of latent radiation in the particulates, hence you want to filter them out, OUTSIDE of where you are if you can to keep them away from you. As chemical threats, the only good news is that they generally dilute and dissipate over time. Unless you are in a confined area, such as a terrorist attach on a subway or tunnel, getting far enough away from the source is adequate if you can avoid concentrated exposure. This means the life of the threat is also short of there is dissipation. A biological threat however, keeping regenerating as it is passed one. The worst part about chemical and biological threats are that unless you are aware of an attack or outbreak (others have already suffered), it will be hard to know when to use a gas mask, HEPA or NBC filters. Instruments what detect these are prohibitively expensive. Fans of the movie Close Encounters of the Third Kind may remember the low tech approach, the “canary in the coal mine”. Canaries die before people do in bad air, or at least in low O2 or high CO2, such as in the coal mines. Also, in the absence of oxygen, fires, such as candles, go out. Simple things to know and watch for.
BASIC LEVEL. – The most inexpensive and simple thing you can do is buy some N95 masks which are available at pharmacies, big box retailers, and hardware stores (or something close people wear for protection from working with fumes and dust).
INTERMEDIATE LEVEL – You can make a simple air filtering system off a vacuum, or inexpensive shop dust collector. Any kind of fan with enough pull to draw air through a filter, like some of the better furnace filters. Plastic and duct tape can do the rest for you to seal off an area if you had to, and blow fresh filtered air into it.
ADVANCED LEVEL – For your home or retreat or shelter, you should have a positive pressure air filtration system in place, provably one that can run on battery backup also, or at least part of it. As for the fallout threats, nuclear, asteroid impact, volcanic, all three of these are really particles that any good furnace filter (short of HEPA) will be effective in removing. Even consider getting a used furnace blower, they can be found cheap, talk to a HVAC guy to buy an old (used) one – in fact consider hiring a HVAC guy to set up a layered system of filters for you for intake in of air from a high level of free particulates. This will clog a single small filter quickly, so you need a lot of draw filter surface area. You also can back flush – use air pressure in reverse to blast clean clogged filters and start over. Consider starting with a fine wire mesh, which you can back flush easily. You probably would want to back flush with an air hose if possible, and moisture may create a paste and clog it up worse.