Just to rule out the keyboard, try disconnecting the keyboard and testing some links. For example, if a shift key, etc. is stuck down, this can change what happens when you click something. E.g. a stuck Ctrl key would cause each click to open a new tab.
Have a look in your Start menu to see if there's anything in there to do with the mouse. E.g. if it's a "Trust" brand mouse, see if there's any item saying "Trust" in it. If so, go into it and see if there's anything unusual about the click options. For example, some mouse software has the ability to redefine the buttons such that a left click performs a double-click, a right click opens Calculator, etc.
You could also try uninstalling the mouse software (if present.) A mouse will still work without the software, but any extra buttons on the mouse may stop. However, if it's the software that's causing the issue, at least this will give you a functioning mouse, assuming it is the software.
If you have another wired or cordless mouse handy, give it a try also.
Another option, but a little drastic, would be to try running a system restore to a date before this issue started happening.