I'll keep this short. The boomboxes are pretty much your stand hidden collectable, of which there are 10. There is one on every level somewhere, and you must interact with each in order to earn the "A Boombox Can Change The World" achievement. By interact, I mean that you need to pick it up (default key F) for it to count toward the achievement. You also do not need to do it all in one run; you can go get missed boomboxes from individual levels and the achievement will pop when you pick up the last one.

This guide will typically have directions to the boombox from the start of the level unless otherwise stated.

Proceed until you get to the funky spiral statue in the three-door intersection.
Go straight through the middle door.
You will find yourself in a room with multiple computer desks and a patrolling guard. The boombox will be on the desk in front of you just as you enter the room.

Go up the stairs in the beginning room.
From the top of the stairs, go through the vent behind the boxes to the left.
Follow the vent to the end and you'll come out in this room. Take the key from this guy, then leave this room through the blue door and take the blue door immediately to the left.
Go through the red locked door in this hallway.
The boombox is sitting on the floor next to the desk.

Proceed until you get to the intersection with the vent in the middle.
Turn RIGHT here and go ALL the way to the end of this hallway. Go through the very last blue door.
You'll be in this messy room. There will be a desk sitting in the middle of the hallway to the left. Jump over it and continue down the hallway, hugging the left wall.
You'll find the boombox sitting on a shelf on the wall next to a friendly fire extinguisher.

Go straight toward the 2-clearance threshold and stand in the intersection. Turn around to face where you came from. Look to the right a little bit.
Go through the blue door to the right. Follow the path up the stairs and around the corner to a little room.
The boombox will be in this little room on a shelf to the right.

From the beginning room, go through the right door on the opposite wall (the one in the crosshairs in the above screenshot).
Go up the short stairway and around the corner. Go through the door straight ahead, ignoring the one to your right.
Disregard the warning of impending doom and drop into the den of woe.
Defeat the Grave Warden to unlock the locked door, then go through it.
Go through this hole in the wall and follow the passage until you come out through a similar hole on the other side.
Drop down this hole that has the useless ladder on it.
The boombox will be at the bottom, next to said useless ladder.

From the beginning, go straight ahead through the door in front of you. Then go up these stairs and turn around to look behind you.
You want to cross to the other side of the gap to the vent. Do this by jumping on the ledges along the sides of the room. Go through the vent and turn RIGHT for the boombox (left for the 'It's Called "Snoooker"' achievement).
The boombox will be sitting on top of some drawers to your right when you come out.

Proceed until you get into the main room just past the Symlink enemy.Go through the blue door on the right and head down the hall into the room with the two Security Spiders.
Climb the potted plant stairway in the middle of the room and go through the ceiling vent. Follow the vent to the end until you fall into a small room.
The boombox will be on the floor in the corner of this little room.

Proceed through the level as usual until you drop down the elevator shaft.
Go through the vent at the bottom and turn right. Drop down into the room below.
The boombox will be on a table in here.

Proceed through this level until the very end, but don't go through the elevator yet.
Instead, turn to either side of it and follow the stairs to the landing above.
Realize you have been lied to your entire life.

Originally posted by Informative Entity:

White doors will never open. If one does, feel free to submit a bug report.

--EOF--

The boombox will be in the den of lies.

Do the stuff and get into the Epilogue area.
Leave the first big room through the blue door at the far end.
In the next room, go through the second portal of lies on the right.
The boombox will be on the desk inside.
Clearly the work of the Illuminati.