My name is very very popular in songs, but, to be honest you get over that and if you like the name go for it. My middle name is the name of a "stripper" in a song and I don't think anyone ever sang that at me.
I know everyone is entitled to their own opinion, but I really cant get my head around people who say there will be a few covertly raised eyebrows due to the biblical reference! And not to use it as a first name. I mean seriously who is going to look at a beautiful baby girl or 2 year old or four year old and think "Shes going to screw up some bloke later in life"! Its ridiculous. I can understand not calling your child Fred or Rosemary if your surname is West but at least that is current and realistic! I dont know a single person who would associate Delilah immediately with the bible. I think it is a beautiful name and am considering it as a first name for my next DC. And the older she gets the less there will be people around who will know the Tom Jones song. I would go for it - there is no sane argument above to warrant dismissing it if you love it!