Software designed for education is usually hopeless as it is too worthy to properly interest students and it is usually focussed very narrowly. Many video games are actually much better, and while I shaln't mention it in my list, games like Nintendo's Zelda and Mario franchises are remarkable for teaching problem solving skills. Don't feel that your child is wasting their time on these games as they may be learning an enormous amount about all sorts of things (aside from murdering goblins, toadstools etc.) which will help them with their education in general and maths in particular.
Euclidea has been this year's obsession for me. It is so simple to use and it will keep you puzzling for hours. It is a website, but also an Android and iOS app. It is free to use, though they ask people to contribute at certain stages and I hope people will do that as the developers deserve our thanks and our money. All of the puzzles on the app can be solved using a pair of compasses and a straight edge (an unmarked rule) though as you progress, certain commonly used combinations, like angle and perpendicular bisectors become available to you. Utterly brilliant and the user interface is peerless.
Geogebra is a horrid portmanteau word (I really loathe portmanteau words: just don't say "ginormous" in my presence, please, as it brings me out in hives.). However, this is a stunning piece of software and it is freely available to all, so all is forgiven in this case. The reason for the portmanteau is that Geogebra is both a geometric and an algebraic tool. You can use it to plot and manipulate graphs but you can also use it to do Euclidean geometry. There are thousands of pre-written resources written using it and the community tends to put stuff out for free. The app itself is also free. Completely free. How, I have no idea, but it is. Thank you Geogebra people!
Autograph is a desktop application which I use a great deal. It is a graph plotting package with a huge amount of sophisticated features. It is much more algebraic than Geogebra and isn't really an equivalent, though they share a substantial intersection. It does cost money but it is an exceptional tool.
I will supplement this page with other apps as I remember or come across them.