No, you do not need a filter. Actually you don't need water movement either.
Same goes for supplemental CO2.
That may sound as a joke but it's true.
Only catch is - what plants you want to grow? And make sure the tank is not overstocked with fish. 10 neon tetras in a 55 is about right to be safe, no more. Chosing right makes things simple.
Also you need to be completely consistent with your fish feeding and water changes.
On a funny note - here in Texas we are about to get rid of all our planted tanks because all of tropical aquatic plants will be labeled illegal by the end of January 2011. Then we can surely try to have special kind of tanks - no filters, no water movement, no CO2, no plants. And discuss this hobby with what's left..