I use a combination of real and silk plants in my betta tanks. Javamoss and Javafern, as suggested by Iggy, are great and easy real plants to keep, along with Anubias, Anacharis, Sword Plant, and Water Sprites. You can find out more info on these, and other plants at plantgeek.com
Also, I have found that my bettas adore the silk Tiger Lotus plant I have in their tanks. They can often be found napping on, or hiding in it.