Playing a typical non objective Katamari goes something like this...

1. Oh look.. I'm rolling a ball.. rolling up the pencils.. the rubbers
2. oh no.. I'm being knocked around by a rat. help help
3. OK.. now I've rolled enough where is that rat.. come get rollled into my ball you *******!!!
4. Now I'm even bigger, where were those kids that kicked me around when I was small. time to roll you up too
5. cars..
6. Buildings...
7. Godzillas...
8. Planets...

It's all about turning the whole play area into a desolate wasteland!