Is it true that women live longer than men? Is there any research to support this?
Life assurance companies (among others) have known for centuries that women, as a class, live longer than men. This is true almost everywhere in the world, although anthopologists can point to a few communities, usually living in conditions of considerable hardship, where it is not the case.
It’s such a well-established fact that it doesn’t need a lot of new arch to support it. Consult any set of life-expectancy tables, such as those linked to here: http://www.cdc.gov/nchs/fastats/lifexpec.htm
My Dad lived to 86 and my Mom lived to 79. I don’t think it is completely true that women live longer than men. I am 73 and have had diatetes II for 22 years and have had prostate surgery but seem to be pretty healthy otherwise. My sister is 75 and is healthy as a 20 year old, so who really knows about who lives longer. If I die before my sister, perhaps you are right. 
I don’t think you can just go on individual anecdotal evidence. Statistically in most countries women far outlive men.
See http://www.cia.gov/cia/publications/factbook/ for stats of each country.
Some countries’ sex ratio 65 years and over:
UK - 0.71 male(s)/female (male 3,895,921; female 5,469,637)
Australia - 0.78 male(s)/female (male 1,059,107; female 1,360,536)
US - 0.71 male(s)/female (male 14,608,948; female 20,455,054)
However there is a discrepancy in some countries, notably:
Afghanistan - 1.06 male(s)/female (male 394,444; female 353,046)
Saudi Arabia - 1.23 male(s)/female (male 334,981; female 275,505)
India - 1.03 male(s)/female (male 24,439,022; female 23,687,200)
I find this curious and don’t know if it is related to the inferior treatment of women (or older women) in these countries, or whether women’s reduced status omits them from census data, or whatever.
Generally speaking, as well as the longevity issue, more males will die in infancy. More men than women are born in (every?) population, but it evens out over time, with women ending in the majority.