Safari on iPhone remembers text that you've input into a form when you make a new page (roughly the equivalent of a "tab" in a desktop browser), switch away, then come back.* It behaves similarly when you switch to a different app (through going back to the Home screen) and then come back to Safari. [Though I will note that it doesn't "remember" such things as a partially-entered URL in the location bar. It should.]
In general, the trend in "nice" apps seems to be very much toward them remembering exactly where you had been when you switch back to them rather than starting back at "the top". This seemed revelatory when the first apps started doing it; now it seems obvious.
Doing that requires a fair bit of work, though, by the app developer... so perhaps Apple could do something with the system frameworks to make that functionality be more "for free" to the developer. When iPhone first came out, developers found out that their apps were completely shut down by the OS when they switched away, so they imagined their apps working the same way as they would on a desktop OS when they get closed and reopened: back to the "main menu". There's no reason that has to be the case, though, if developers just persist the relevant bits of the user's state when they switch away then restore it gracefully.
* in general; if memory is running low, Safari will "forget" everything about other pages, so if you were writing something substantial, it'd be best to remember to Select All + Copy before switching away. This is unfortunate.
In general, the trend in "nice" apps seems to be very much toward them remembering exactly where you had been when you switch back to them rather than starting back at "the top". This seemed revelatory when the first apps started doing it; now it seems obvious.
Doing that requires a fair bit of work, though, by the app developer... so perhaps Apple could do something with the system frameworks to make that functionality be more "for free" to the developer. When iPhone first came out, developers found out that their apps were completely shut down by the OS when they switched away, so they imagined their apps working the same way as they would on a desktop OS when they get closed and reopened: back to the "main menu". There's no reason that has to be the case, though, if developers just persist the relevant bits of the user's state when they switch away then restore it gracefully.
* in general; if memory is running low, Safari will "forget" everything about other pages, so if you were writing something substantial, it'd be best to remember to Select All + Copy before switching away. This is unfortunate.