A few years ago , I went through a complete BBA bloom in my tank. This is when I was leaving the light on all day in a room that also had some natural sunlight, and changing the water once a month. After taking a sanding tool to all of the driftwood to remove the algae, performing regular water changes and regulating my light, it got a lot better, but it didn't go away completely. It was then that I started planting my 92 Gallon bowfront, because the workers at my LFS told me that the plants would compete with the algae for nutrients. I've never used (and don't plan to use) CO2.
I started with Java ferns, and kept adding other low light plants (Water Sprite, Water Onions, Anubis,etc) and I seem to be close to having some sort of balance right now. The remaining BBA has been dying for the last few months (I think, it's turning grey and transluscent), and I haven't had much new algae growth. A few more plants and another bristlenose pleco or two, and I think that I will have solved my algae problem.
Here is a thread with some pics of my tank as it is right now. I'm sorry I don't have any pics of the tank when it was in full BBA Bloom. It was EVERYWHERE!
http://www.aquariacentral.com/forums/showthread.php?t=243650
I would have to say from my own experience that planting heavily in non-CO2 tanks can definitely help to combat algae growth.