While I was looking at Untangle again, I followed Simon's documentation back to the 'original' version named Planarity and written by John Tantalo. It's a bit different to Untangle in that it presents you with levels of increasing difficulty and awards you points based on how fast you solve each level. And it's up to you to decide when a level is untangled - you have to click on the 'done' button rather than having the program auto-detect when the puzzle is solved.
Play Planarity in your browser by clicking this link.
Also at that site there are a couple of versions for iPhone - which I've not tried.