Artichokes are a plant which means that they can be included as part of a Paleo-friendly life-style. Full of protein, fiber, and a number of necessary micronutrients, this particular plant has been shown to raise HDL and lower LDL, leading to lower rates of atherosclerosis and heart disease. It also contains properties which may be beneficial in promoting healthy gut bacteria and aiding digestion.
In some places, the flower portion of the artichoke is made into an herbal tea. This has no known benefits, but neither is it harmful, so if you find it, feel free to try it without worrying about straying from the Paleo path. Mark Sisson has a whole post about the health benefits of artichokes.