You start off by choosing a type of animal to herd. These could be real animals or could be similar to real animals but more quirky (and therefore fun). You can start with 15 hens or 8 sheep or 6 pigs, etc. You then are given a top-down (or possibly zelda-style top down-ish) view of your herder and your animals.and you've just to get them from one side of a map to the other. All fine so far, yes? This is the gist of the single-player version. With each trip across the map, you get a gold coin which you can use to buy more animals or customise the ones you have (spray-paint the sheep, buy a new smock for your herder, etc).
The main bit of the game comes when you go online. Each install of the game has a unique map which is your own home field. When you go online, you can either invite people to come to your field or you can wander off to other people's fields and interact with them. An interesting bit of it is that you can leave your herder and herd to wander off themselves. If you're on a desktop, your herder wanders off whenever the screensaver comes on and you can choose to passively watch as it interacts with other herders on other machines, if you've got a mobile device, you can choose to send your little guy off when you close the game and the central server will track interactions while you're offline. When you start up again, you can choose to see where your herd went. There's also the possibility of having a flash piece which will just let viewers on the website passively watch.
I think it would also help if there was some system in place so that people's fields could be next to each other, you'd wander off the side of your field and into your neighbour's. If the neighbour stopped playing for a while, the next new player would move in. That way, you could zoom out and see the entire game world.
It's not as simple idea as my last game design (blob-pushing-around touch-screen, flash crossover thing) but that one has been done now (by someone else). I did actually make this game (above) about seven years ago and it was surprisingly fun but I didn't have the marketing budget to promote it (i.e. none). There are some interesting algorithms you can implement in order to get good herd behaviour. It doesn't need to be strictly accurate so you can get some cartoon-ish wandering-off, notice herd is far away, running after them behaviour.