Is there a mouse that has extra buttons that can be programmed so that
when I press one of those extra buttons it is equivalent to having
held the Control Key + clicked the Left Mouse button (the same for
Shift + left mouse button, etc)?

Howdy emanquestion-ga,

The following will fit your needs perfectly.

Kensington PilotMouse Optical Pro (5-button)
http://www.kensington.com/html/4006.html

"The PilotMouse Optical Pro features a refined shape and cushioned rubber
grips that put all 5 powerful programmable buttons at your fingertips."

Kensington PilotMouse Optical Pro Wireless (5-button)
http://www.kensington.com/html/4007.html

"The PilotMouse Optical Wireless features wireless connectivity, a refined
shape and flexible rubber grips that put all 5 programmable buttons at your
fingertips."

Google's own Froogle's search result by price shows it can be had for under
$20.00 from several online sites.
http://froogle.google.com/froogle?q=Kensington+PilotMouse+Optical+Pro&scoring=p

If you are into gaming at all, you can pick up the mouse plus the game of
"Splinter Cell" for under $10 more.
http://froogle.google.com/froogle?q=Kensington+PilotMouse+Optical+Pro+%22Splinter+Cell%22&scoring=p

One caveat is that this mouse might seem large, but one gets used to it
relatively fast.

If you need any clarification, please feel free to ask.


Search strategy:

I use the above mouse and made sure it could be programmed in the manner
that you requested.

Looking Forward, denco-ga - Google Answers Researcher

thanks.

My pleasure, emanquestion-ga, and thanks for the 5 star rating.

Looking Forward, denco-ga - Google Answers Researcher