Can you update your game after publishing?

i was just wondering if you can, because i need to know if i need to make a lot of levels overtime or right now

What are you making it for? Android.. iOS? Ect... answer should be yes... android make sure you keep your keystore safe and the same.. DO NOT DELETE OR OVERWRITE IT.... Google will not let you update it without compiling against the same keystore.... somebody may be able to answer the other targets

Updates on iOs are straightforward. You compile a new version (Make sure to change version numbers), register it in Connect and upload it. It then appears as an update on App Store.

Flash works fine as well...

How does it work on desktop though? If I change something and make a new version, will people have to download the entire game so they can update it?

Desktop Mac works like iOs if you use AppStore. Updates are  published and installed auto or manually.
Windows works the same through Windows App store. If you install outside this I´m afraid users will have to download new release and update.

what about directly do a website?

what about directly do a website?

Flash? On a website?  Id think you update the swf file on the website, and when the webpage loads, it'll be the new game.. that's what the flash games in the forum posts do