How do songs trigger memories associated with previous experiences of listening to the  song? Background:
If I like a particular song, I listen to it while doing other things until I get sick of that song. This creates an extremely strong bond between the two things: the song and the activity. The activities usually being programming languages or video games. Whenever I hear the song again, the emotions and/or visuals of whatever I was doing flood my brain, and I can remember them vividly.

Questions


How does hearing a song trigger memories associated with that song?
Is there anything special about songs and memory associations?
Has any particular research been conducted on the association between songs and memory?
I believe this phenomenon is well known in cognitive science. That is how our memory works.

The simpliest explanation would be the Hebbian learning rule: "Neurons that fire together, wire together." So, you can imagine some neurons firing when you hear the music and some when you see the game. Now, if these used to fire together, they are probably connected. Somehow you've learned that these stimuli come together and your brain is recalling them all even if this time only the audio stimulus is presented.

Try reading more about episodic memory:


  For example, memories of people’s faces, the taste of the wine, the music that was playing, etc, might all be part of the memory of a particular dinner with friends. By repeatedly reactivating or “playing back” this particular activity pattern in the various regions of the cortex, they become so strongly linked with one another that they no longer need the hippocampus to act as their link, and the memory of the music that was playing that night, for example, can act as an index entry, and may be enough to bring back the entire scene of the dinner party.
  Episodic and semantic memory


However, auditory triggers are possibly not the strongest available. According to an idea called "Proustian phenomenon" the strongest would be smell.
Example study to that matter:
Proust revisited: Odours as triggers of aversive memories



Reference:

Toffalo, M.B.J., Smeets, M.A.M., van den Hout, M.A. (2012).  Proust revisited: Odours as triggers of aversive memories.  Cognition &amp; Emotion, 26(1):83-92.