Only if you and your significant other are legally married. So, if it is a male/female relationship you are inquiring about then things are pretty straightforward from the marriage standpoint. If it is a same sex relationship you are inquiring about then things get more complicated. Same sex marriage is an issue that is still being addressed on a state by state basis. If your home state does not recognize same sex marriage and your employer is domiciled (incorporated in, established in) in such a state then you can't get married in that state anyways and an out-of-state marriage in a state that does recognize same sex marriage is not recognized in your home state.
There is a tremendous amount of litigation going on in the Federal courts over this issue which makes it hard to be totally definitive when addressing this question. To make things even more interesting, you might work at a branch location of a company domiciled in a state that recognizes same sex marriage while your state of residence still doesn't. And your employer's policy may be to accept same sex spouses as dependents under their group health plan. This can result in the situation where one same sex couple (you still have to be married but I've got some neighbors that went out of state to get married in a jurisdiction that does allow for same sex marriage even though our home state currently does not) may be able to take advantage of their employer's health coverage while a similar same sex couple across the street who work for employers headquartered in states that don't recognize same sex marriage can't cover their same sex spouse as a dependent. It is an interesting time to be in the employee benefits business.
There is a tremendous amount of litigation going on in the Federal courts over this issue which makes it hard to be totally definitive when addressing this question. To make things even more interesting, you might work at a branch location of a company domiciled in a state that recognizes same sex marriage while your state of residence still doesn't. And your employer's policy may be to accept same sex spouses as dependents under their group health plan. This can result in the situation where one same sex couple (you still have to be married but I've got some neighbors that went out of state to get married in a jurisdiction that does allow for same sex marriage even though our home state currently does not) may be able to take advantage of their employer's health coverage while a similar same sex couple across the street who work for employers headquartered in states that don't recognize same sex marriage can't cover their same sex spouse as a dependent. It is an interesting time to be in the employee benefits business.