Although handy, after a short period of time, that constant clicking can become the bane of one's existence when working on a project or playing a game for more than 5 minutes. Luckily, it isn't difficult to get rid of that incessant clicking in most cases, and doesn't affect the performance of the mouse in a negative way. In fact, it can actually enhance the ease of the scroll wheel
Step 1: What you'll need
A mouse to silence
A phillips head screwdriver
Needle nose pliers (not always needed, not shown)
Step 2: Crack it open
Step 3: The insides
Once you've gotten the mouse open, take a quick look around to locate your scroll wheel, it should be glaringly obvious. If you have an optical mouse, just pull it up out of its bracket, making sure not to loose any of the springs attached to it. The wheel on the optical mouse can be pulled out by pulling it sideways from it's post. I've found it best to remove the PCB board from the plastic tray to do this. Most aren't screwed on, but some may be
Keep in mind that not all mice are exactly the same, so use your head when it comes to taking apart anything internal, or you may be purchasing a new mouse very soon.
Sorry for the shakiness of the second image, The lighting was bad and the auto focus wasn't working well because of it.
Step 4: Silencing the wheel
If you look carefully at one side of the scroll wheel in the non-optical mouse, you'll see that it's spoked. These spokes are the reason for the clicking. Now, instead of breaking all of the spokes out, we'll just take the little spring that hits each spoke as you rotate the wheel. If you have the Dell mouse that i'm using, you'll notice that there are two springs, one wraps around the post in the center of the wheel, and one is situated in the small plastic piece the wheel rotates around. Leave the first one alone, it aids in clicking the scroll wheel down. Just take the one that goes inside the wheel out. Once the spring is gone, just nest everything back together and slide the scroll wheel assembly back into place
If you have an optical mouse, notice that there are little metal arms that warp around the post that the axis of the wheel was through, you can either pry these open with a screwdriver, or use needle nose pliers (which i found easiest) to open the enough to pull the post away from the arms, and remove the black plastic wheel, and metal insert the makes contact with the grooves in the wheel. once you've taken the metal insert out, replace the black plastic wheel and use the pliers to put the metal arms back in place. After the post is secure again, push the wheel back where it was.
This will require some force, but don't go crazy, as we're dealing with small plastic parts.
Step 5: Reassembly
I've noticed that the metal insert that we took out of the optical mouse acts as a spacer so that the scroll wheel doesn't make contact with the plastic. If your scroll wheel seems to be slower, look at the hole in the top and take some sandpaper to it if necessary.