Is there a way to easily record a phone conversation in-progress?
There are a couple of apps to try.  I use Ultimate Voice Recorder which costs $4.99 but works beautifully.  You can start recording in the middle of a call.

A quick search on AppBrain brought up Record My Call which is free.  I haven't used Record My Call so I can't comment on whether or not it can start in the middle of a call.

Update: Ultimate Voice Recorder does record both sides of the conversation.