I use this for a number of things...

One of them is to adjust stereo placement. Using the track's pan control always leaves one side tied to the extreme edge. i often want a particular width where neither side is an edge... This has been my on,y way of achieving this...

Keni

I use it to narrow stereo piano sounds that stretch from left speaker to right speaker.  Recently, I used Channel Tools on a cover of Drift Away where the stereo piano was interfering with the guitars that are panned left and right.  In the original the piano is located left of center.

I use it on a stereo track to take out some of the mid signal sometimes. I find it works great with stereo reverbs to leave room for the center elements like vocal and snare. I used to use it to narrow and pan stereo images, but ever since I downloaded Flux's free Stereo Tool, I use that instead. It has two rotary knobs to pan the left and right sides (which I prefer over Channel Tools' sliders) and it also has a "morph" slider so you can create two settings and morph between them. So for instance you can start with the track in mono and gradually morph it out to full stereo at some point in the song. It's a cool effect which is really easy to do with Stereo Tool.  

It's my most-used of the bundled plugins and, aside from Pro-Q, the only plugin that finds its way into every single project. If it's got piano, organ, sampled guitars or synth pads, they'll normally all have Channel Tools on them.
 
Mostly, I use it for stereo panning as described by dlesaux above. But I also use it for both narrowing and widening on occasion. Usually not on the master bus, but often on sub-busses. I often automate the Angle parameters to give the mix some motion.
 
Yes, M/S balance can be beneficial on reverb returns to clear out the center for vocals. I don't do that unless it's a very busy mix that also needs a lot of reverb - and that's rare because the first thing I do with a busy mix is cut down the reverb.

I use it for stereo panning of the brass sounds, trombones and lower instruments for a tight stereo spread within the total field of keyboards and drums.

The Console can change polarity on only an entire track. Channel tools lets you throw only the left or right channel out of phase, so you can cancel common elements to those channels while leaving non-common elements intact. Also with a stereo track where each channel comes from a different mic, you can tweak the delay time for one of the channels to reduce phase issues when the mics are at different distances from the source.

I use it always to cut solo and bass instruments from the sides and I also cut often backing instruments(not bass) from the middle. I read that tip from some mag years ago.

I did use it for adjusting stereo width but now mostly use WAVES S1 because it's got way more options to adjust the stereo field ...
 
BUT - I now use it a lot for quick timing corrections ... let me explain: quite often vocalists are just a tiny bit too early and "delaying" the take by just a few ms sometimes makes a huge improvement to what it feels ... Channel Tools gives you a dial where you adjust the amount of the delay without noticable overhead and it has what must be a logarithmic dial i.e. it's very sensitivity in the small range (so you can delay by just a few samples) ... it is also very helpful to illustrate to musicians that it sounds better if they don't rush the take ... and once they've heard it, they can often play it like you want it ...
 
likewise, you want the bass or the drums to be just a notch behind the beat ... Channel Tools in the bus and off you go ...
 
Unfortunately, using automation on the delay doesn't work too well because it can give you click/pops/artifacts even when adjusting delay in silent parts of the take ... so for final corrections of timing it still means split and nudge ...