Washable Filters are thick and catch a lot of particles out of your air, however they also restrict air more than other filters and if not cleaned regularly will often not clean out again. These filters are really only an option when you have plenty of extra return and you wash them religiously.
We all know these, they are the cheap see through filters you can get at a discount. These filters are better than nothing but not better than much of anything else.
The ridged pleated filters are a good option for most homes. The 1" ones are most common although they come in thinker sizes. These filters will read as a 90 day filter but that is in a perfect environment. Chances are your home is not a perfect environment and you need to check them once a month.
These are the thicker pleated filters. They are a great option for replaceable filters; the only downside is that with a lifespan of 3-4 months they often get forgotten about and not changed.
These are an accordion looking filter that is folded out and often held in place by plastic combs. They are a great filtration option usually doing slightly better than a 4 inch pleated; they are kind of a pain to change out but do provide an extra layer of filtration.
The best of the best in filtration, there are many options discussed in the electronic filtration section. If your allergies or breathing is an issue this may be an option you want to look into.