iTunes music and video: Sync or stream
The cornerstone of the Apple ecosystem is iTunes, which started as a music library and repository but has grown to include videos, podcasts, e-books, ringtones, iOS device backups, and the amazing iTunes U free courseware library. There is no equivalent for iTunes in any other ecosystem. No self-respecting Apple user would stoop to playing the file-copy game via USB or SD cards to sync such files.
But Google does offer the free Music Manager app for OS X and Windows that syncs your non-copy-protected iTunes music with the Google Play online service that can then stream or download via Google's Google Play store to your Android smartphone's Play Music app. Your Android device likely has other music apps on it, such as from its manufacturer, which can be confusing. Play Music is Google's standard music player, which ties into the Google Play service. Ignore your device's other music apps.
For music, free Google Play service works like Apple's $25-per-year iTunes Match: You upload your music to Google Play, which then can stream it to any Android device that is tied to the same Google account. Apple's iTunes Match downloads any songs to your iOS device that you want to play, making it permanently available on that device. Google Play streams any music to your device unless you explicitly save it to the device (through an unintuitive but simple process). Thus on Android, you need to be careful about burning up your cellular data plan from music streaming. Fortunately (like iOS), you can set the device not to stream or download music unless you have a Wi-Fi connection.
Google's Music Manager runs in the background on your computer; as your iTunes library changes, new songs are uploaded to Google Play, making them available to your Android smartphone. Playlists are also sycned, but not smart playlists or podcasts. That means music on Android gets close to the no-brainer it is in an all-Apple environment.
Video is another story. To get videos onto your Android smartphone, you can buy or rent them from the Google Play Store, downloading them to the device over Wi-Fi -- similar to how iTunes Store's video service for iOS, OS X, and Windows. But you can't sync the videos in your computer's iTunes video library to your Android device, as you can to an iOS device. The same limitation applies to photos.
Unless, of course, you get a third-party utility. Samsung offers the Kies utility on the Galaxy S III, and you can download the Mac or PC client from Samsung. It's sort of a poor man's iTunes, syncing music, videos, photos, and podcasts, as well as contacts across Kies-enabled devices. It can even import these items from an iPhone, iPad, or iPod Touch, as well as from any libraries on your computer. Kies works both over USB and via Wi-Fi (for Android devices that have the Kies client installed, such as the S III). Note that the Kies client did not work on OS X Mountain Lion until just last Thursday, when Samsung issued a compatibility update. Kies works OK, but it's clunky compared to iTunes.
A better and popular iTunes equivalent for Android is DoubleTwist, which comes in three parts: the free DoubleTwist Desktop for your PC or Mac, the free DoubleTwist Player for your Android smartphone, and -- if you want to be able to sync over Wi-Fi rather than just a USB cable as well as stream to an Apple TV -- either the $5 DoubleTwist AirSync utilityor the $10 DoubleTwist Pro Player (an in-app purchase that also allows podcast syncing) for your Android smartphone. My only caution about DoubleTwist is that it tries to access your contacts, which it has no need for to do its job; OS X Mountain Lion automatically alerts you to this attempt and lets you block it.
To use the free DoubleTwist syncing, you need to connect your Android smartphone to your computer via a USB cable. If you have a Mac running OS X Mountain Lion, you can't do that -- USB syncing between Macs and Android devices doesn't work with OS X Mountain Lion. This is true even if you install Google's free Android File Transfer utility for OS X. (Windows needs no transfer app; it has built-in drivers for Android devices' storage access. But you still need an app like DoubleTwist to do more than see the Android device as a storage device.) DoubleTwist users can use the $5 AirSync add-onto get around this USB issue in OS X Mountain Lion.