Since we didn't have Christian radio around here for my musical-preference-forming years, I tend to think in terms of albums rather than singles.
I've noticed through my quick perusal of the replies that the majority of people choose a Praise & Worship song as their favorite. So in that genre I'd choose the "Hungry" album by Vineyard UK. That one came out in 1999, before P & W became the revenue-engine and "out of ideas" fall-back that it is today (think Rebecca St. James or Newsboys). I mean, how many different recordings of "God of Wonders" does the world really need, since none of them are as good as the original anyway(the first City on A Hill being another good album)?
I've also noticed that a lot of people choose generic pop like Casting Crowns, Jeremy Camp, or Mercy Me. That's fine of course, but if you've heard one song by these guys you've pretty much heard them all. Before they "made it big," Mercy Me had a few independent albums. One of them is called "The Worship Project," it has the original version of "I Can Only Imagine." I suggest that their fans try to find this album, so you can hear what a creative and interesting band they were before they were commandeered by the Nashville Music Machine.
I've also noticed a lot of people choose fluff-pop like Avalon. Again, that's fine, but I like more meat and less bubblegum. So here are some of my favorites, in no particular order:
PFR: "Goldie's Last Day" and "Great Lengths"
Sixpence None the Richer: "The Fatherless and The Widow" and "This Beautiful Mess"
Adam Again: "Dig"
The Choir: "Circle Slide" and "Free Flying Soul"
The Lost Dogs: "Little Red Riding Hood" and "The Green Room Serenade"
Steve Taylor: "Squint"
I'm also enjoying "Live from Nowhere vol 1" and "Ohio" by Over the Rhine. That's all I can think of right now, and yeah, it's all old except the Over the Rhine stuff, but there are probably some people who wouldn't consider that to be "Christian music" anyway.
Andrew