The International Student Identity Card (ISIC) is available through www.isic.org. It can help travelers obtain discounts on public transportation and admissions to museums. Any official-looking university identification may (or may not) be accepted as a substitute.
An HI card, available at any HI hostel (www.hihostels.com), will get you discounts on your stay at any HI facility. The HoLa (www.holahostels.com) card works in a similar way for a different network of hostels.
Travelers over the age of 60 can sometimes obtain senior-citizen discounts on museum admissions and the like. Usually a passport with date of birth is sufficient evidence of age.