you can do as much as the apps allow you to, so just search the net for ipad apps that do what you want the ipad to do, like a shopping list app etc. Aside from that the default apps are for social networking, music, movies, and the browser. Everything else you need some app to do it, for example I can use my ipad to plan a flight with an app called ForeFlight it's really good for pilots and the best app i've seen for that purpose.
so in short it can do a lot depending on what you need, it is limited by apple to use iTunes to buy more music and movies but there are ways around that too.