Vertical Mouse
At Google, I used an ergonomic mouse, and the one that Google has available is the Evoluent Vertical Mouse (on the right in the picture). I liked this mouse enough that I got one for my personal use as well. It In terms of functionality, it does everything you would expect (left, right, and middle click, scroll wheel, move the cursor just like a regular mouse), and it is very easy to switch over to it from a normal mouse. It has a configurable resolution, but I always use it on the highest setting. One annoying thing is that one of the thumb buttons is configured to go back in a web browser, and I never intentionally press it, but I sometimes accidentally press it.
In terms of ergonomics, this mouse is probably the best that I've tried. When you use a normal mouse, your wrist is rotated from a neutral posture, so it's constantly in tension. In the vertical mouse, your wrist is in a neutral handshake posture, so it's not in tension. In a normal mouse, you will probably have your wrist fixed to the table (or, just as bad, resting on a wrist rest). This means that you will probably do all of your mousing using your wrist, which makes it more likely for your wrist to get a repetitive stress injury. With the vertical mouse, you can't really rest your wrist on the table when using it, so you are forced to use your elbow and shoulder and leave your wrist resting. Also, with a normal mouse, long periods of mousing (eg, gaming) might leave your finger on your mouse for a long period of time, which is bad. With the vertical mouse, you will probably leave your finger slightly to the side except when you are actively clicking. The most noticable benefit for me was that it forced me to stop leaving my wrist in a fixed position, but I have noticed all of the benefits I mentioned.
One thing to note is that using your shoulder rather than your wrist is a bit of a double edged sword. Your wrist is more precise. When I played League of Legends, a fast paced, competitive online video game which involves a lot of quick mouse movements and clicking, I did find that I was a little bit worse with the vertical mouse. The ergonomic benefits outweigh the video game detriments, and it wasn't a huge difference, but it was certainly noticable.
Trackball
Despite liking the vertical mouse, I hadn't tried a trackball mouse before, and there are also ergonomic reasons to like those, so I got the CST2545. It's made in America by Clearly Superior Technologies, the build quality is high, it's supposed to be very durable, and I have heard great things about the customer service as well. The picture on the website makes it look like a normal sized mouse, but it is totally not normal sized. It is huge.
I was expecting to have a large learning curve before I got up to speed with a trackball, but the CST2545 was actually extremely easy to use. After browsing the internet for a few minutes to get a general feel for the mouse, I fired up League of Legends. Surprisingly, even though I had used the CST2545 for under a day and I hadn't used a trackball before, I was playing as well as normal by the end of the game. I was probably better than with the vertical mouse. After three or four games, I think I was better with the trackball than with a normal mouse. I think that it's so nice is because it's really easy to quickly stop the trackball and to move the opposite direction (eg, quickly moving the mouse to the top of the screen so that you can see farther up, and then moving the mouse back to the middle of the screen) and because it requires less physical motion to move your cursor in general.
Surprisingly, while it's good enough for gaming, it feels a little less precise in day to day usage (eg, selecting one line of text in a paragraph). That could be because I use the mouse a bit differently when playing LoL than when mousing normally. In LoL, you mostly use right click, and there are few instances when you need to left click, and most of those are low stress things that you can take your time doing. As such, when playing LoL, I use my ring finger for the right click, and I use my thumb, pointer, and middle finger on the track ball. With normal computing, I use the thumb for the left click and my pointer and middle finger on the trackball (plus my ring finger sometimes). In any case, I'm still experimenting with it, so it remains to be seen whether using it for day to day tasks is an enjoyable experience.
Ergonomically, it doesn't have the same set of benefits as the vertical mouse, and I have noticed that a bit. Since I'm still getting used to it, I'm not sure whether or not it is comfortable to use.