I have had repeated and consistent success removing stuck CD's using variations of the following method. I'm not certain why this works, but it has never failed me, is reasonably quick, and always releases my pent up frustration about the fact that the disc is stuck.
It works better in the winter.
When CD's become stuck, turn off the radio. Turn off the car. Leave the car outside overnight to get nice and chilly. With the ignition off, press and hold the eject button until it beeps. With a fist, firmly (not too hard!) strike the dashboard near the CD player, causing a mild tremor in the CD player while the player is trying to eject the disc. For some reason this always gets the disc past the "stuck" point and out in to my hot little hands. The player seems to be fine after this as long as the disc (which is typically too thick) is not reinserted.
I discovered this method after a stuck disc spontaneously ejected when I started the car on a particularly cold morning. (It was stuck there for a week!). The next time it happened, the fist encouraged the disc to come all the way out.
I suspect that removing the player and placing it into the fridge or freezer overnight might work for those of you in a cold climate. Be warned, you risk incurring dew and frost all over the inside of the player, so maybe do this as a last resort if disassembly is not your cup of tea.
Nate