A Hostelling International (HI) card is useful for discounts at official HI hostels. An International Student Identity Card (ISIC) doesn’t get anywhere near as many discounts as it once did – none, for instance, are available on public transport.
Some museums and sights offer discounts to senior citizens, though to qualify you may not only need to be senior but also a citizen.
If you’re visiting lots of the national parks and historical sites run by the Israel Nature & Parks Authority (INPA; www.parks.org.il), you can save by purchasing a Green Card, valid for 14 days, that gets you into all INPA sites for just 150NIS (a six-park version costs 110NIS). With membership of the Israel Society for the Protection of Nature in Israel (www.natureisrael.org) you'll get discounts on accommodation at field schools and outings.