מגן אברהם: "נוהגין להעמיד אילנות בבית הכנסת ובבתים"
However the custom was put a stop to by the Vilna Gaon (Gra) due to the similarity to Christmas trees. I for one am all for adding some real trees to my local synagogue. I'm willing to forego the flashing lights, and stars at the top.
(you can see sources here)