The Pixel 2 and 2 XL have a nifty always listening music ID feature. You can simply look at your phone and see a "Now Playing" notification that tells you if the phone has heard a popular song. Google doesn't keep a log of the songs you encounter, but you can do that yourself with IFTTT.
IFTTT user hypnopompia created an applet you can add to your IFTTT account right now. It uses the Android notification service to watch for the Now Listening notification, then it logs the content of that notification to a spreadsheet in Google Drive. You need to enable notification access for the IFTTT app on your phone, but no other setup is required.
I've tested this applet, and it works surprisingly well. It typically fires a few seconds after a song is detected. The spreadsheet just has two columns, one for the time/date and another for the song name/artist. This is a great way to check up on the songs you encounter throughout the day. There are some apps to do this, but the spreadsheet is available online.