It is fairly common for co-workers to date each other. Think about it: you work in the same office for 40 or more hours per week. People are bound to develop feelings for each other and want to see how those feelings might evolve if the two were to start dating. Most companies allow relationships in the workplace, so long as they are disclosed to human resources. So, is it inappropriate for one co-worker to ask another out on a date?
Many companies, in an effort to prevent sexual harassment, have created policies that set forth rules for dating in the workplace. These policies might go as far as banning co-workers from dating each other if they aren't already in a relationship. Others simply require couples to disclose their relationship to human resources.
Asking a co-worker for a date can be considered inappropriate if the person asking does so in a distasteful manner or continues to ask for a date after being turned down for a date. If you are asked out on a date by a co-worker and it makes you feel uncomfortable, let them know this immediately.
Even if you tell the person requesting the date that you are unavailable that night or are quite busy in your personal life, this should be viewed as giving a 'no' answer. Again, a simple question requesting a date should not be inappropriate if the person asking does so in a respectful manner.
Relationships in the workplace can be challenging, especially if one turns sour. It can lead to poor productivity and even public disagreements between the two people. Morale can suffer greatly and other employees might feel uncomfortable. Despite all of this, as long as the request for a date is done respectfully, it is not inappropriate in the workplace.