I think it would be difficult to work with the person who I'm dating. I love my partner and all but that would be a LOT of him. Also having to deal with him in work situations - like what if he isn't getting something done that you need, I just would prefer to keep work as work and home as home.
Although quite a few of my coworkers have met their partners at work. Actually three of them. One is engaged, one has been dating her partner for about two years, and the other one is still a newer relationship but it has to start somewhere, right? The one in a new relationship, her partner recently left the company. The others still work there. It's interesting actually. Sometimes it gets a bit weird/awkward with the two who work very close.
I guess it depends on your plans, how much you like the person, etc.