For our wedding, a friend gave my husband and I this Cutco cheese knife: http://dishtable.com/images/T/4-09.jpg It does wonders on fresh mozzarella!

I put it in the freezer for about half an hour before I plan to slice it.

I've seen the freezer trick work but I usually just use the same knife I ue to slice tomatoes, it's very finely serrated so I don't have to apply very much pressure. I was given it as part of a set but it's also sold separately for pretty cheap.
http://www.sears.com/kitchen-aid-kitchenaid-ka2truk5e-serrated-utility-knife/p-SPM5694183003P

I find that a serrated knife works best for something like this.

an egg slicer!

Dental floss

thin, very sharp knife, sawing motion with light pressure.

An electric knife works really well.

A good sharp knife. Do the paper slicing test. If it doesn't go through clean, sharpen that bad boy. Should do fine.

But yes, dental floss works great too for clean cuts but is a little tougher to get even slices from a round ball (this is the best way to cut cinnamon rolls too!)

Guitar string.

Echoing offbalance's tip for a serrated knife.

Also, I tend to cut the whole thing in half first, which tends to take the pressure off when cutting it and lends itself to smoother cuts.

If you eat fresh mozzarella often (Yay!) then you can invest in a specific knife from any gourmet store (Williams Sonoma, any good cooking supply store) that is more like a wire string. Some have multiple "strings" on them that work like an egg cutter or an avocado slicer and they make quick work of an entire mozzarella ball.

Dental floss is the best option. It also works for slicing a cheese cake.

I also use a serrated knife and I give the mozz a quarter turn every couple of cuts. It might not make a huge difference, but I feel like then if it gets squished, it at least gets evenly squished?

egg slicer. genius.

Have you tried using a steak knife? I prefer the buffalo mozzarella, which you can just tear with your hands.

I have a bunch of Kuhn Rikon paring knives (I think the line is called Colori) with non-stick coating. I find that the squishing is usually due to the freshly-cut surfaces of the cheese dragging on the smooth surface of the knife, and the nonstick ones help (though I guess in fairness it's not perfect; I usually also try to reassemble the slices as I go and hold the ball together to minimize deformation). I have also had decent results with a serrated knife (Wusthof bread knife), but you can get some tearing around the edges.

If you cannot accomplish it successfully I saw some fresh mozzarella presliced in packaging yesterday at my local grocery.......