The most important piece of equipment is the helicopter, and that's provided by your outfitter. Various companies use craft ranging from Bell JetRangers to Eucoreil AStars, but the brand probably isn't as important as having a craft that's well-maintained and equipped with appropriate safety equipment, such as fixed floats or an inflatable flotation system if you're going to be flying over bodies of water. Obviously, you also want to have an experienced pilot who's certified under the Federal Aviation Administration's fairly stringent Air Tour Safety standards. The pilot should give you a brief but thorough primer on safety before you fly.
Another crucial piece of equipment that will be provided by the tour operator is a federally-approved life vest (or a "life preserver," as the FAA regulations call it). There are noninflatable and inflatable life vests, but the latter, which don't take up much space until you deploy them, probably make it easier to get out of a copter in case of an emergency water landing. You also need to have a device that's adjustable to fit your dimensions. If you want to be totally prepared, buy your own. One manufacturer, Life Support International, makes the $269 HV-35P Helicopter Passenger Vest, which has dual flotation cells that can be filled either by manually releasing a CO2 inflator or, if that fails, by blowing into the tube.
What sort of actual fishing equipment you use is up to you. Some helicopter fishing outfits will supply you with lightweight spin casting or fly fishing gear, which is all you need if you're going trout fishing. But you're usually welcome to use your own equipment, so you might as well. If you're going after salmon, for example, be sure to bring along some heavier gear.