I use a pretty long winded but free way. I load up the audio clip into Audacity and highlight a thin instrumental section, possibly just the melody playing etc.. I then go to Analyze > Plot Spectrum. This will bring up a graph showing the frequencies present in the song. Change the setting from 512 to 16384. Now the graph will be very jagged and harsh, you can clearly see the peaking harmonics.
Make the window as big as you can and begin to move your mouse over the peaking frequencies. Write down what note it is and go along the graph, writing down the peaks; until you have a full octave of peaks.
You can then begin to suss out the key from the notes you have jotted down.
Long and time consuming I know but it works for me, hope this helps.