In the summer, Israel is hot and dry. You will need a wide-brimmed hat and cool, loose clothing. Everyone in Israel dresses very casually, so your main concern is comfort for days spent walking. Women will need to be sure and bring modest clothing that covers their shoulders and knees for entering holy sites.
In the winter, Israel is cool and often rainy. Bring warm clothing and a raincoat, if possible.
You will also want to bring a small satchel or backpack for carrying essential items on day trips. Another handy item to have is a water bottle carrier. Especially in the summer, you must carry at least a liter of water with you to avoid dehydration and sunstroke.
If you forget anything, you can easily buy it in Israel, but the price may be higher than at home. You can find more information on what to pack here.