Israel is a very casual country, and comfort comes first. For touring in the hot summer months, wear cool, easy-care clothing and sensible shoes for walking. If coming between May and September, you don't need a coat, but you should bring a sun hat that completely shades your face and neck. Take one light sweater for cool nights, particularly in hilly areas (including in and around Jerusalem) and the desert. Also take long pants to protect your legs and a spare pair of walking shoes for adventure travel or hiking shoes for more serious hiking. A raincoat with a zip-out lining is ideal for October to April, when the weather can get cold enough for snow (and is as likely to be warm enough in the south for outdoor swimming). Rain boots may also be a useful accessory in winter. Pack a bathing suit for all seasons.
Note that many religious sites forbid shorts and sleeveless shirts for both sexes, so a light scarf comes in handy to throw over the shoulders. Women should bring modest dress for general touring in religious neighborhoods.
Along with a sun hat, take sunscreen, insect repellent, and sunglasses in summer. Essentials such as contact-lens solution and feminine hygiene supplies are available everywhere but are more costly than in North America.