Android apps have an "allow automatic update" checkbox. If the box is checked, and the new version of the application has the same permissions as the old one, the application auto-updates.
There is notification (and AFAICT, no way to turn it off in the Froyo version on the original Moto Droid), but otherwise, jellicle is correct. Just check the box on the Android Market App page to allow autoupdating.
Would be interested to learn what the "security reasons" are that you referenced above; did you mean the underlying OS? I've always felt that by Appifying more of the core Android OS functions, Google could deliver more timely updates because they would be able to avoid many of the carrier restrictions and awful modifications made by manufacturers (e.g. just include the keyboard as an app that gets shipped with the core OS).
[UPDATE:] Can't reply to georgemcbay, but he stated:
> "this can be disabled"
I've had this set in the market app as you described for a while, but still get notifications when an app has autoupdated. Did I miss something?
Froyo added auto-updates that work as jellicle described (you select it as an option per-app from inside the market app and it'll auto-update those apps that publish new versions whose permissions haven't changed).
It is true that by default you still get notifications for each app update, but this can be disabled (go to the settings in the Market app, set the notifications setting to 'Do not notify me').
While technically this isn't quite the same as Chrome because the user has to disable notifications manually (and the notification option isn't a per app option, but rather for all apps), I think the system in place on Android strikes the right balance for a mobile device.
