Depends where you work... I've dated someone I worked with - and am still with him. Longest relationship by far. We both have the same belief: Work is for WORK and outside of work is the social/relationship life. I'm very strict on it. He also was working in a different department, so I caught glimpses of him now and then but didn't have to always be around him. Now he works elsewhere, because it is a better source of income.
I did date someone before from a previous place I worked... And he could not wrap his genius mind around WHY I leave work as WORK. So he ended up irritating me, if anything.
So there are two sides to it... One good, one bad. But, also realize if you work, hang out and even live with someone ALL THE TIME eventually you are desperate for a break. Both of you need space... Your own space! It puts a strain on the relationship to always be around each other (for most people anyways). If wanting to date someone who you work with, also keep in mind if it does not work out.
And I can tell you, that "genius mind" I dated, didn't think it was at all awkward. I broke it off with him, not the other way around. I did not find it awkward either, though found it amusing that he had a burning desire to "make me jealous" (didn't work... But... Whatever.)