Cruciferous vegetables have recently been confirm to have powerful cancer fighting power. It's not limited to just broccoli, there are many tasty vegetables like Swiiss chard, broccoli, cabbage, Brussels sprouts, cauliflower, watercress, radish, rapini, arugula, spinach, turnip, kale, and bok choy, so they're easy to eat regularly without getting bored.
Early research has shown anti-cancer activity, and research is on-going. Some anti-cancer properties include: protect ing cells from DNA damage, helping inactivate carcinogens, antiviral and antibacterial effects, anti-inflammatory effects, inducing cell death (apoptosis), and inhibiting tumor blood vessel formation (angiogenesis) and tumor cell migration (needed for metastasis).
Cancer.gov has more information about the status of research.