Sometimes it depends how close you guys are and if he or she even likes you back, But honestly I say go for it you can't go through life wondering how it would be if I did do it, You have to go through life wondering what if I didn't do it...
Don't dip your pen in the Company ink! Haha just kidding, I married a coworker :-) It's nice to always have that in common, we can always talk about work and understand what the other is talking about. When I was single and dated outside of work, they'd have no idea what I was talking about if I brought up my job.
If the relationship goes sour, the work enviornment isnt going to be pleasant anymore. I'd keep it just as friends and if you guys are both mutually really into each other and think its worth an effort, find another job. Other people will get into your business too and even if you split, who knows whos going to be the one that starts drama or spills secret information that was meant to be secret. I guess that would depend on your age group and if you work with mature adults. It could only be a good thing if you guys could stand working together say if it ended in marriage. Some people love working together and others need their work to be seperate because if you see each other too much then you will get tired of each other fast and start fighting. Then work/pleasure would be combined and you'll be up each others butts all the time and stressed out. If you're just looking for a hookup, then its a definate noooo!!!!!! You could also ruin it for her and make her lose her job.
I met my husband at work. We've been married for 25 years now. Just be mature about the situation. Does the co-worker seem interested in you? If so ask away as long as your jobs aren't placed in jeopardy. If not then don't ask, it could make for an awkward situation for the person. Good luck