You might want to double-think that filter thing.
Water filters can build up bacteria (listeria is not a fun thing - there are others, too - some pretty bad); this can cause everything from a "funky smell" to "go to emergency room or die". That said, tap water in most municipalities is pretty damn clean, and you can run without a filter; but if you don't want to change the filter, then do just that - remove the filter, so that you don't give the bacteria a nice growth area. If you do change the filter, don't go more than a year between changes at most. Most filters are cheap enough, usually less than $50 USD.
As far as the air filter - well, I've never heard of one on a fridge - but if you have one, it's probably to filter the air before it gets to the fan that cools the compressor. If you let it get super dirty, it won't move the air, and your compressor will be overheated/overworked, and it's life will be shortened, or it will fail - or the breaker on the fridge (know where your's is?) will trip. And don't take the filter off and just run filterless - because now the cooling coils will act as the filter, and they are anything but easy to clean (because if you don't, again failures will eventually occur - nbtw, that they sell a special fridge coil cleaning brush that looks like a very narrow bottle brush).
If you're talking about other filters in your house (HVAC) - then you want to change those too, fairly regularly. If you don't, again, you'll be overworking your A/C unit, plus the air won't be moved around effectively (making the unit run longer to cool/heat - increasing your bill). Plus, those filters get pretty nasty too - and that stuff doesn't stay on the filter.
They make reusable filters - you cut them with scissors to match the filter opening, then when you are ready to clean them, you take them outside and run a water from a sprayer hose "backwards" thru the filter, then let 'em air dry. That can be a cheaper and easier alternative to holding on to a box or two of filters (though such filters are pretty cheap).
Finally - note that on many cars (not all!) there is a "cabin air filter". Check your manual on how to replace it; most people don't know about that filter, but it isn't difficult to change out. Costs of course are variable, depending on the car. Again, though, if you don't replace it regularly, your cabin heating/cooling will suffer, air flow will be reduced, the fan motor will have to work harder, etc.
Basically - for air filter, check them now and then. When they look like they are getting overly fuzzy, or you can't see thru 'em - change them out.