For purposes of this post, "childhood" means age 13 or younger. I'm not talking about "kiddie" songs either.
I grew up in the 80s, so...
Cyndi Lauper - She Bop (1984). I was five years old. This is the first "favorite" song I can remember having. Of course, at the age of five, I didn't know what it was actually about...
Dire Straits - Money for Nothing (1984). Or, as I called it, "the MTV song." Every time the video came on TV I would not move until it was over. The video got me interested in computer animation, as well.
A-Ha - Take On Me (1985). Another song I like because of the video, which is my favorite of all time.
Tears for Fears - Shout (1985). Tears for Fears was, mysteriously, my favorite band when I was six.
The Pretenders - Brass in Pocket (1979). Although I didn't hear (or pay attention to) this song until I was seven. I've been a Pretenders fan since then. I remember my mom playing her Get Close tape in the car when I was eight, and then when I was thirteen and finally had my own radio/tape player, stealing that tape to listen to.
The B-52s - Love Shack (1989). Yes, I know it was fucking everywhere, but I loved it when I was ten and I think I still love it.
REM - Losing My Religion (1991). Saw the video when I was eleven or twelve years old and the song blew me away. I will never get sick of it.