I see trackballs have been mentioned, so let me get a few words in for them.
First, unlike traditional mice there are several different types of trackballs. You've probably seen a trackball that has a large central ball that you use your palm or fingers to move. These are usually used for work that requires high accuracy. Second type has a smaller ball in front and is operated by index and/or middle finger, you have button placement that resembles traditional mice. Third type has ball where your thumb is located and obviously the ball is operated by your thumb.
When Kazan mentioned Logitech Trackman series, last two types belong to the Trackman family. What Kazan missed that no Trackmans are currently produced. The only Logitech trackball that is produced now is the M570, a thumb operated trackball. I just so happen to use the M570 at home and at work. I have not used traditional mice since I got my M570's. I use the M570's for everything, including games and I'm no worse off than I used to be with old mice.
All my life I had used only regular mice, at first I really couldn't use these M570's accurately or comfortably. After a few days use I adjusted and using them started to feel more natural and comfortable. After a few weeks my accuracy was only slightly less than I used to have with regular mice. I once tried to play a game using a regular mouse and I totally sucked, I've gotten used to the M570's. A lot of people won't even give trackballs a chance because it's not what they've gotten used to. I was very skeptical at first, but now I couldn't go back. Hell, I don't even want to.
I'd argue that my M570's are more accurate than any Logitech and Razer mice I used before. And best of all, I don't need to move my hand or wrist around to move the cursor. That is a significant amount of strain off from my hand and particularly wrist. Instead you use your thumb to move the ball. It's more comfortable even. The M570 is wireless but batteries can last well over a year, true story.
Like with usual Logitech mice, you can use Logitech software/drivers if you want to. But it's not necessary and I actually prefer to use without. The Logitech software uses its own cursor acceleration methods even if you set it to use Windows standard and I hate Logitech's cursor acceleration. I much prefer to use Windows' own "enhanced pointer precision" with mice and trackballs alike.
So my suggestion would to try out the M570 for two weeks. If you can't get used to it, then so be it. But if you do, you might never want to use traditional mice again. If you do get M570 or any other thumb-operated trackball, my suggestion would be to pay attention how you place your thumb on the ball. I've found that for me that best position is to keep the ball under the joint. Trying to control the ball with tip of your thumb doesn't work, at least for me.
Right, so I've only given praise for the M570, anything bad about it? Well yes there is. Remember the mice before they became optical? They had balls underside that accumulated crap over time and you had to clean them and the chassis every now and then to keep movement smooth. Same applies here too. You gotta keep the ball and its chassis clean, otherwise accumulated dirt will hamper movement of the ball.
http://www.logitech.com/en-roeu/mice-pointers/trackballs/devices/7365