The website below has links to lots of free maths games. Not all of them are non-flash but in the subjects I looked at I found at least a few.
Also, we have used the website Kidsgraph:
There are two versions and I found the Classic one easier to use.
There are lots of apps that allow you to practise a specific skill but not always at the right level and are only useful when you are looking at that skill. To give you an example, I was teaching about fractions and hadn't yet got onto the link to decimals but in the only app I found that was not bad for fractions, the learners had to understand equivalency, the link to decimals and how to convert between decimal fractions, fractions and to work out equivalency of both at the same time. This limits considerably when it will be useful.
Some of the arithmetic apps are really good for tables and basic mental addition, subtraction and division but the progression in difficulty doesn't really push primary 6's. I do like Mathsboard, particularly because they can show their working and explain their methodology.
What is really needed is a more comprehensive app that allows for progression of skills. What we probably need is something more like a mathletics or sumdog approach where there are lots of different maths and numeracy topics for the children to explore and that go beyond the basics or something like the BBC learning games, I guess that would be expensive though.
My partner's friend said that his daughter is really enjoying the app Playful Minds which I have had a quick look at and seems to have a much wider subject matter. It is for 5-8 year olds and you create an avatar and can collect rewards, a bit like Club penguin or Webkinz. It would be worth thinking about what kind of resources developers could produce that would be useful in schools for maths and numeracy.
Maybe other people have suggestions on really good maths apps that they have found?