Yes. You and your spouse can separately opt into a Flexible Spending Account if your employers offer an FSA.
However, you cannot apply both flex spending accounts to the same expenses.
Important Limit Change
For plans years starting after December 31, 2012, contributions to an FSA are limited to $2,500 per person. Married couples can therefore put away $5,000 maximum. After December 31, 2013, the $2,500 limit will be adjusted for inflation.