R. Profitt and DarkHawk are right. This is what is said in the Logitech knowledge base:
Question: ''When I move my cordless mouse, it moves the cursor on the system next to me. What should I do?''
Answer: ''This is called ''Cross talk'' and is characterized by one cordless device controlling the cursor or keyboard input of another device connected to a different computer. To avoid possible interference, try to keep the distance between systems at least 10 feet. Also, moving the mouse closer or further away to the receiver can also improve transmission and performance. If the above fails, try pressing and holding the ''Connect'' button on the receiver for 10 seconds. This will reset the receiver's connection information and allow you to do a first time connection with the receiver and mouse or keyboard. After holding the Connect button for 10 seconds, then press the Connect/Channel button on the bottom of the mouse to synchronize it with the receiver. If you have a cordless keyboard instead of, or in addition to, a cordless mouse, press the ''Connect'' button of the receiver again, then press the ''Connect/Channel'' button on the Keyboard. Perform these same steps on any other Logitech cordless devices in the area that are experiencing cross talk. Another step that can be tried is to remove the batteries for 15 minutes. Then re-insert them and boot the computer up. It is important that during this time, you do not press the connect button on the receiver or keyboard of the other cordless desktop system.
I could not find anything on mouse crosstalk in the Microsoft knowledge base. Perhaps the problem is not so common for MS mice because of their more limited range.
Buying a new mouse was suggested. This may or may not work if you bought a new Logitech mouse, as it could wind up on the same troublesome frequency. Of course, if you replaced the Logitech mouse with a Microsoft mouse, their limited ranges might eleminate the problem, even if they used the same frequency.