The Stora Kopparberg mining company has existed since it was granted a charter from King Magnus IV in 1347.
A few banks tend to last for a long time [1]. Banca Monte dei Paschi di Siena has existed for about 540 years.
Beretta, the italian firearms company, has existed for 486 years (and has been family owned the entire time).
East and West Jersey were owned by a land proprietorship for around 340 years starting from King Charles II bestowing the land to his brother James in 1664. [2]
At first I thought multinational corporations would be more stable because they could move from land to land to avoid wars and such. But apparently they haven't lasted nearly as long as their single-nation counterparts.
The Knights Templar were granted a multi-national tax exemption by Pope Innocent II in 1139, and lasted almost 200 years until most of their leadership was killed off in 1307.
The Dutch East India Trading Company was one of the first [modern] multinational corporations, spanning almost 200 years from 1602-1798.
However, the longest-lasting companies have been family owned and operated. [3] [4]
It appears most all companies that have lasted a long time are due to two factors: dealing in basic goods and services that all humans need, and looking ahead to the future to change with the times.
[1] https://en.wikipedia.org/wiki/List_of_oldest_banks [2] https://docs.google.com/viewer?a=v&q=cache:nYQU4NpfD74J:... [3] http://www.businessweek.com/stories/2008-05-14/centuries-old... [4] http://www.bizaims.com/content/the-100-oldest-companies-worl...