Is there a way to see a list of all the apps available on the app store?
As far as I am aware Apple itself limits this to category. I think they have specifically not included this option to make browsing the AppStore a simpler process for not technical people, which is the bulk of their target market. Therefore even iTunes doesn't have an option to do this yet.

I use an App called AppShopper which allows you to search for specials, and also specify which categories you want to see. I haven't used it in a while but if I recall it does have an option to list all applications in all categories.