Is there a way to display the currently-playing track on my Mac? I would rather not use a 3rd-party app.
This uses a 3rd-party tool, sorry, but it works very well. It's called Now Playing and it displays the current track via the Notification Center (both a pop-up and a persistent message in the NC itself). I use it on iTunes 10.7 and OSX 10.8.2 (ML).
I found another App that does the same sort of thing but is Open Source and purports to use fewer resources. It's called iTunification. It also supports Growl, in addition to Notification Center.
You can click the Zoom button in iTunes to get a Mini Player version which you can position anywhere on your screen.
In iTunes Preferences - Advanced, you'll additionally find an option to keep the Mini Player on top of all other windows.
You might wait until the new redesign of iTunes gets released. It was said to come this month (October 2012) so you might only have to wait 30 days if it ships on time. The new mini player window seems to do exactly what you ask.
In the mean time, this Take Five app is superb and really is useful all the time. I got it on a whim and it's really something I have come to love for how easy a timer it is. I find myself using it all the time to remind myself to do something when the music starts again.
If you want to display the notifications manually and not every time the track changes, you can assign a shortcut to a shell script like this:
IFS=$'\t' read -r artist track < <(osascript -e 'tell application "iTunes" tell current track to artist & tab & name end tell') || exit terminal-notifier -title "$artist" -message "$track" -group itunestrack
terminal-notifier can be installed with
sudo gem install terminal-notifier.
Go to Window and select Switch to MiniPalyer. If desired, in Preferences > Advanced select "Keep MiniPlayer on top of all other windows"