My son is now my carbon copy mini-me, but when he was younger, he looked EXACTLY like my partner. The LC, the nurses, and the OB (who signed the forms for delivery of the sperm!) told us in the hospital, "Wow! he is a perfect mix of you both." We would look a little confused and say something like, "yeah, we must have really hit the jackpot because we tried to find a donor who looked like C." The health care professionals were all mortified. When a close friend would comment on it, I would usually say, "yeah, I think C must have spit in the vial."
We get tons and tons of questions about DS "looking like Daddy" which I think are usually motivated by people trying to figure out what his ethnicity is--he is obviously mixed race, and people want to know. I usually say, "Well, his donor was African American, but we don't know what the donor looks like other than obviously being really tall and absolutely adorable!" We try to model language and responses for DS as he gets older. Now that he is older, he usually announces with some scorn, "I don't have a dad!" and the person gets really flustered and looks my wedding ring, and stammers, so I say, "No, no, it's fine! you would have no way of knowing I am married to a woman. DS was conceived with donor sperm."
My brother gets it a lot with his three children who are also mixed race. People are rude--"Where did you get them?" "they look nothing like you." (they do, except for their Asian features). I usually smile and say, "Their mother, my SIL, is from Hong Kong." My brother says, "My wife is from Hong Kong." My mom is more apt to tell people to go suck it.
My favorite story was the time my partner (AA) and my 5 year old niece (Asian) were walking hand in hand at a neighborhood festival near my dad's house. An older white woman came up to my partner, "Oh, she's beautiful! Where was she born?" and my partner looked absolutely confused and said, "ummmm, Scarsdale? I think..."