Google didn't make the iPod, so it never needed to make its own iTunes, and so Google doesn't have control over a bit of software with which almost every gadget-buying person in the world is familiar. That, in a nutshell, is why it's so freaking complicated to sync up your Android device with your computer to transfer music or files.
Android is a wide-open system, but wide-open can be more complicated than narrow. There are many kinds of Android devices, and at least three major computer operating systems. Some phones try to make syncing simple, by automatically prompting you to choose what kind of files you're trying to send; sometimes it works, and sometimes such steps make the process even more confusing.
In my years of using Android, I've narrowed down the pain I'm willing to endure to transfer files to and from Android. Here are the best tools, in a short list, that I recommend for transferring music, photos, and files between Android and systems.
Windows: Grab doubleTwist and/or WiFi File Transfer. The doubleTwist Windows/Android app combo works just fine for music and videos over a USB cable, and if you want to make syncing automatic and even easier, you can grab AirSync to automatically send new files between your computer and phone or tablet, whenever they're in the same Wi-Fi area. As for photos, I like Picasa, another Google product, that's very good at finding photos on Android phones and transferring them to your computer (or to Picasa Web Albums).
If you need to trade more than just media files, plug in your phone and see if you can explore it as if it were a USB drive. Some phones make this very easy; others require setting the phone to "File transfer," and others just generally don't connect easily. To work around USB problems, grab WiFi File Transfer, one of the best reviewed and most-installed Wi-Fi-based file apps in the Play Store. It's very simple to use, and free to try for files up to 4 MB in size.
Mac: Again, doubleTwist to the rescue, at least for music and movies. For photos, I'm sticking with Picasa, though iPhoto has been known to work cooperatively with certain Android phones when plugged in.
If you need more robust file transfer, you can go the WiFi File Transfer route, as noted above, or install a little helper app: Android File Transfer for Mac, made by Google. Install it, and whenever you plug in an Android device by USB, it should pop open and act just like a Finder file browser.
Linux: Nothing is ever that easy on Linux, is it? There are apps and tools available (like the aforementioned Wi-Fi file tools), but I've found that you're better off working at a deep level, to make sure your Linux device can see Android and recognize it and get at its files. Start with Step 3 in the Android developer guide to USB devices. Basically, you run a
lsusbcommand, look for your Android device in that list, copy its four-character ID code, and then create a new "rules" file that, at boot or service startup, knows to look for your phone and give it the proper permissions.
Once you're set up, you can use many music manager apps to access your tunes. What about other files? You'll need to install MTP support in your system, because newer Android phones don't use the standard USB mass storage protocol. Here's a write-up on how to install MTP in Ubuntu and connect through it; other Linux systems should work in similar fashion.
That's the bare-bones guide to connecting to Android files from most systems. What did I miss? Comment here, or tweet at me.