I've been to Israel about ten times, and each time was different. Sure, there is a feeling of wariness brought on by all of the publicity in the media regarding the conflict in Israel between the Jews and the Palestinians, but I never felt threatened during any of my visits.
About that media, interestingly enough, I just looked on CNN's world headlines, and the top world stories today are about Kenya, Sri Lanka, Australia, China, the Arabs, Peshawar, and Colombia. I had to dig way down into the Middle East section to find that at least 17 die in Gaza violence. The conflict between the Israeli government and the Palestinians still runs strong, but since it's old news, no one pays attention.
If you are planning to visit Israel, pay attention. Stay away from areas of unrest (the Gaza strip along the Mediterranean coast in the south and the West Bank areas, especially), and you should have no trouble at all. Israel needs tourism to survive, and tour operators go to great lengths to protect their trade and those who visit Israel.
(The first rule of staying safe is: Don't stand out. Try not to look like a tourist. (The typical American tourist wears shorts, t-shirts, and baseball hats. Comfortable, casual, and even trendy clothing is not a problem in Israel, but men and women almost never wear shorts or baseball hats. If you want to blend in, stay casual, but choose jeans or pants, long sleeve shirts, and full, long skirts for women. This will allow you easy entrance into the religious sites, and if the material is light cotton, it will keep you cool and protected from the sun in the summer). It might help to check out some photos of what the locals are wearing these days. And by all means, don't hang your camera around your neck. Keep it in a shopping bag (everyone shops).
(Of course, if you are in a tour group, you're going to stand out.) Even so, the safest way to visit Israel is in a tour group. (You have safety in numbers, so don't wander off.) Often vendors will try to get you to come into their shops when a tour is walking through an area. If you stop, you can quickly get left behind, and not know which way they went. Your tour guide will often let you shop in a certain area, and have everyone meet at a specific location at a certain time. Follow the guide's directions. Some tourists are happy to stay in the group and are too timid and afraid they'll get lost if they strike out on their own. Other tourists with a healthy dose of wanderlust will want to explore on their own, which is ok to do, even in Israel, if they follow a few rules of common sense)
If you are (traveling) on your own, don't attract attention. Never drive a rental car into one of the areas of unrest. Study a map, and know the areas to avoid, especially if you are on your own.
Learn a few local words, and use them sparingly. Or better yet, don't say anything if you can't tell the difference between a Jew and an Arab. Saying Shalom, to an Arab will not help you blend in.
Put the phone number for the local embassy (U.S., if you are American) in your phones speed dial. Be sure to have the number for Jerusalem's U.S. consulate or Tel Aviv.