Actually, the assumption is that those born before 1957 have immunity by actually having had measles (and mumps, but not rubella). However, if you are not sure that you actually had measles, then that may not apply to you.

Some measles vaccines given from 1963-1967 were less effective or ineffective, so revaccination is recommended in that case. Pre-1979 mumps vaccine has similar issues.

http://www.immunize.org/askexperts/experts_mmr.asp

For an individual born before 1957, ask yourself (for each of measles, mumps, and rubella) whether you had the actual disease or have had the vaccine other than the less effective or ineffective types. If not, then it may be worth considering getting the vaccine.