It may seem odd to suggest a bathing suit as the first item to pack for visiting a country named Iceland, but the wonderful pools and hot spring baths are a joy to experience. Layering is the secret to comfort in Iceland, so bring a waterproof, wind-tight jacket or shell, regardless of season. In winter, bring a good, heavy coat.
Durable, broken-in walking or hiking boots with good ankle support are needed for hiking (forget tennis shoes for this), and a telescoping walking staff might also prove handy. If you'll be going to the highlands to ski or snowmobile, be sure to bring good gloves. Likewise sunscreen and sunglasses are a must to protect against the low, lingering sun of spring and fall, which can be a real bother to drivers. Sweaters are useful—perhaps why Icelanders are so good at making them.
If you're a sports enthusiast, note that all fishing tackle, riding tack, and riding garments should be certified sterile by a veterinarian or doctor unless it is obviously new and unused. If not, gear will be cleaned at your expense upon arrival, or impounded.