There are hiking tours available on the Big Island that are suitable for most levels of stamina. Those with disabilities, lung conditions or recent injuries are not advised to take these tours, although with the recent decreased activity, air conditions have improved.
At the very least, you need to be able to walk in wet areas, with rocky uneven terrain, and small changes in elevation without a problem. Some of the shorter waterfall and bird watching tours are suitable for almost anyone.
For the people wanting a more challenging hike, look for the ones that go deep into the Volcano park, as well as the ones that climb the summit.