Arguably the most common fruit that grows on palm trees is the coconut. But did you know that palm trees also provide a number of other delicious fruits? With the right species, you can enjoy dates, peaches, and even acai. It should be noted that in most situations palm trees won't live long enough to flower and produce fruit if you keep them indoors. You should really only expect fruit if you're planting your palm trees outside.

Source: Fast Growing Trees