How can I record Skype conversations?

You can use Skype Call Recorder. It can

• Record calls to MP3, Ogg Vorbis or WAV files
• Automatic and manual recording
• Configure automatic recording on per-caller basis
• Split stereo recording

and it's free.

You can install it by adding the ppa:

sudo add-apt-repository ppa:dajhorn/skype-call-recorder
sudo apt-get update && sudo apt-get install skype-call-recorder

(Update 14.08.2015: The ppa does not seem to work any longer. Go to http://atdot.ch/scr/download/ download the appropriate .deb and install it with gdebi skype-call-recorder-ubuntu_0.10_i386.deb)

Now you can open the program from a Accessories folder and should appear in your system tray. From here, you can open Skype and the call recorder will interact with it while it's running. You'll be able to choose your settings from the menu and set up recording. Here are some FAQs from the website.

Just use this package

Select these two checkboxes and select User defined audio source from drop-down.