Look at my 5gal paludarium thread in my sig. I started that tank with a filter and it has been unfiltered for over a year now. Its possible to run a tank stagnate and keep it balance, its not ideal or easy though. My paludarium clicked pretty quick, water is clearer then some of my filtered tank and it does not get the scum on the surface even though it is stagnant. It however is only inhabited by snails and shrimp since under 1 gal. It also gets very rare water changes 3-4 months.
My newer 15 gallon was torn down and setup this way only about a month and a half ago. Its still establishing its balance. So far its going good. Its based off the walstead method but I am using a lot more light and stocking heavier. Used dirt and sand from my yard. Currently has 3wpg of T8 and spiral compacts combined. Really no algae to speak of yet. Slight particulate in water, but not really any worse then the other filtered planted tanks. Power head in this tank directs water up to break the surface. Keeps the layer of scum at bay, which is due to nutrient imbalance and should disappear on its own once tank is more established. It looks kinda green in the pics, but is not that bad in person. My crappy lights leave a lot to be desired though
. Everything in this hobby is about finding the right balance. A filter can be seen as a imbalance if you want. The only reason a filter is needed is because more nutrients get put into a tank then it can consume. You can get rid of this by adding only enough nutrients that the tank can consume. A lot believe this means low stocking, but the reverse is also true. Make the tank consume as many nutrients as you are adding. This can be done by lots of fast growing plants under the right conditions and you can maintain a heavy bioload because it is needed to feed a tank with a heavy nutrient demand. Plants prefer ammonia above any other nitrogen source, so simply they eat the ammonia and no nitrate is produce from this process. They are in the end more efficient then a filter. Coming back to the topic on this thread though, plants are dependent on light. They still consume nutrients at night. But if left in the dark for a long time their nutrient uptake will be reduced greatly