It depends on the species. According to UMI's handbook, a worker ant can live one to two years from birth.
Many ant workers live less than a year as adults. Pharaoh ant (Monomorium pharaonis) and ghost ant (Tapinoma melanocephalum) live only a few weeks. Queens of these species live less than a full year. Colonies of these two types are almost constantly producing new broods of queens, males, and workers to keep up with the mortality. By contrast, workers of many mound ants (Formica rufa and relatives) and cornfield ants (Lasius niger and relatives) live 1-3 or more years and their queens may live over ten years. These types produce queens and males only once a season. The record appears to be a queen cornfield ant caught just after mating, which went on to live 22 years in a lab colony, producing fertile eggs until the last few months of her life. --Dr. Ant