Met my husband working for the same company. It was around 100+ employees, and we worked the same schedule and technically were in the same department, and were friends for several months before we started dating. It was awesome as we got to spend time together just working (sat within talking distance), and on our breaks and hang out after work. As we lived on opposite sides of town, this meant that we didn't see each other as much if we weren't working (hour + drive to each others' houses).
I left the company for a better opportunity a few months after we started dating, and we ended up moving in together and getting married after a year or so. Would have been nice if we'd actually moved in together while still working together to save on the commuting costs! ;)
I honestly don't know that I would do it again without knowing that we'd end up married, but probably? It really was one of those things where we both knew really early on that we were going to be best friends and end up together.
Disadvantages... well, if you break up, you still might have to work with that person, so I'd be REALLY sure that dating is something you just have to try. You might get sick of seeing the person every day (or not - I didn't), and you might get really sick of lapsing into "shop talk" while out together. You'll have to worry about coworkers gossiping or pestering you about your relationship, and you definitely will have to make sure you stay professional at work as you'll be under more scrutiny if coworker relationships are not actually banned (and in that case, worry about keeping said relationship a secret from other coworkers if you are prohibited from office romances).
Definitely work on hanging out as friends first to make sure you both are a good match. If you go out with a small group of coworkers as friends, that gives you a chance to develop a deeper relationship and realize if you do want to take it to the next level; that's what the husband and I did. Hang out as friends first with other friends, then see where it goes from there. There's less pressure for things to work out too if you get to know each other a bit more as friends before jumping into dating.
I've seen office romances work out beautifully, but also seen several blow up in a huge mess and result in one or both of the people leaving or getting let go for inappropriate office behavior. I think it really depends on you and the intended datee's personality - can you both handle a relationship at work, will you be okay working together in the event that things don't work out, etc...