Cases vary of course but a lot of apps will break at some point if they've been orphaned and there's an OS upgrade (or, as other comments note, an online service has been sunsetted).
I expect the majority of apps I downloaded on my 1G iPad would not work today on a current iPad if not upgraded but if there's no server component, they'll presumably continue to work on the original platform.
Comments
Cases vary of course but a lot of apps will break at some point if they've been orphaned and there's an OS upgrade (or, as other comments note, an online service has been sunsetted).
I expect the majority of apps I downloaded on my 1G iPad would not work today on a current iPad if not upgraded but if there's no server component, they'll presumably continue to work on the original platform.