Until Google+ adds such functionality, we've found five workarounds that will help you record your next Hangout — for free.
"ScreenCastle gives you the ability to record your entire screen, or to change the size of the recording box by pixel dimensions. An unlimited service, ScreenCastle will tape from the moment you hit record until you're ready to stop. You then have to upload your recording to the site."
Pixetell apparently records until you stop it, and "offers direct uploading to YouTube. As far as exporting goes, you can grab your files in FLV, AVI, MOV, OGV and WMV formats. Although it's such a fantastic tool, screen recording is just one string in the Pixetell bow — we'd recommend checking it out."
Screenr "only lets you record for up to five minutes. Recording is browser-based and instantaneous, and you can resize the recording window to suit. Once your five minutes is up, you can add a description to your clip, then sign into Screenr via one of your social media accounts for built-in sharing to Facebook and Twitter, the option to publish to YouTube, to generate an embed code, or to share the Screenr URL directly. As far as downloads go, you can save the MP4 file down to your computer."
FlashBack Express apparently records till you stop it, "is a free download for Windows users ... Once you've recorded your clip, you can then view it in the player. You might find the basic edit options handy, like the ability to upload directly to YouTube or to export your video as Flash (both SWF or FLV) or AVI.
Screencast-O-Matic is the Jeff Lebow option. "The free version limits recordings to 15 minutes. Recordings have a Screencast-O-Matic logo on the bottom right of the video. If you want to lose the logo you can upgrade to Pro for just $12 a year, which also gives you advanced editing options. It also means your recording time is limited only by local disk."