There is no difference in life expectancy between left and right handed people. There was a controversial study done in 1980 by Halpern & Coren that suggested left-handed people had an average life expectancy of 9 years less than right-handed people. However, data was based on second-hand information: surveys from the next-of-kin of recently deceased persons asking about right/left handedness and age of death. They found left-handed average age of death was 66; right-handed average age was 75.
Unfortunately, this study keeps getting quoted even though more recent data has shown their hypothesis is not supported. Second hand survey data is not a sound methodology.
In addition, if a study reports a higher mortality rate (or any other "problem") in left-handers, then it's very important to look at the research design and how the data was analyzed. Simply checking the sample sizes will give a good indication of whether it was a "real" significant difference. If the sample sizes are large, and most studies have sample sizes of 1,000 or more, then there will be a "statistically" significant difference between groups (i.e.: Left versus Right) even if the amount of variance explained by the two groups is very small, which means there is no clinical significance. A statistical significant difference does not mean it has clinical or meaningful significance. Many statistical tests will give a significant difference only because of large sample sizes. Therefore, the measure of explained variance needs to be computed because it is unaffected by sample size.
More recent studies have disputed the notion that left-handed people die earlier. For example, see the study by Aggleton, Bland, Kentridge, & Neave in the British Medical Journal at http://bmj.bmjjournals.com for more information. In addition, for a discussion of the Halpern & Coren study, see the link: http://bmj.bmjjournals.com/cgi/content/full/308/6925/408