Chrome Remote Desktop is free but I've never really been able to get it to work (though never really tried).

I used to use LogMeIn until they started charging an arm and a leg.

join.me is free, but it's mainly designed as screen sharing software - you need to have the remote user manually give you keyboard/mouse control.

GoToMyPC.com is free for 30 days and costs $12/month after that. Probably your best bet.