First off, an update: I have fixed the iPod, sorta. It's still not perfect, but I can put songs on it and I'm back to just coveting this one rather than actually needing it.
Now then, a few words on head songs. Songs that get stuck in your head. They've been around forever, of course. I'm sure as Martin Luther was nailing his 95 Theses to the door of the Wittenberg Church, he was really thinking "Goddamn, why can't I get that one Latin hymn out of my brain?" Followed immediately by, "Oh crap, I'm totally going to Hell for thinking 'goddamn'. I better finish this up and go self-flagellate." However, I think that the recent influx of catchy indie pop/rock songs has really exacerbated the issue. You can't avoid hooky singalong stuff anymore by just not listening to Top 40.
Some examples of what I'm talking about. Some of them are downloadable, but don't come crying to me when you're forced to re-enact the last scene of Pi to recover your sanity.
Belle & Sebastian - Storytelling
Rilo Kiley - Portions for Foxes
Arcade Fire - Neighborhood #3 (Power Out)
Futureheads - Decent Days and Nights
Bright Eyes - I Must Belong Somewhere
Loquat - Swingset Chain
The Decemberists - Shiny (I mentioned this one a couple months ago, but in my head it remains)
And then there are mash-ups, which are totally the "new thing" even though they're about as new as representative democracy. Nonetheless, there are some good ones here, and they are also highly subject to stuck-in-head syndrome.