Do you get sound in any apps e.g. Music and Videos apps but not in your other apps ? If you do, then have you got notifications muted ? Only notifications (including games) get muted, so the iPod and Videos apps, and headphones, still get sound.
Depending on what you've got Settings > General > Use Side Switch To set to (mute or rotation lock), then you can mute notifications by the switch on the right hand side of the iPad, or via the taskbar : double-click the home button; slide from the left; and it's the icon far left; press home again to exit the taskbar. The function that isn't on the side switch is set via the taskbar instead : http://support.apple.com/kb/HT4085
Found the fix.
If the reboot doesn't fix it.
If the headphoens work find, but no external speakers.
If the double-click and page right to the software mute, doesn't show the sound knob - just the brightness
If your pop-up shows "Docking Station"
Then, the problem is very likely a dirty connector. The iPad/iPhone/iPod connector uses a resistor value to determine if the device is connected to an external 'speaker'. There are a range of resistances, for a range of products. This is known as the Connector Pin 21 issue.
Take some windex on a que-tip, or perhaps a Windex paper scrub and rub it on the bottom connector port. Somehow, "something" has gotten on those contacts, and it is pulling the voltage on pin #21 down - so that the iPad "thinks" it's connected to an external speaker - this will disable the internal speaker circuitry, as well as the internal speaker volume controls.
Do not over-saturate and short out your iPad. Do not throw it in the sink, do not use the kitchen faucet to flush it out. A Que-tip with a few drops of Windex (or other gentle cleaner) should work just fine. Takes all of 30 seconds - and magically, the volume knob appeared and everything worked just fine.
I had the Same problem. Headphones worked, but without I only had very limited sound. No keyboard clickers, no sound to my games or videos, but I could hear my songs. After rebooting several times and also cleaning the docking port, I remembered that I've recently changed the mute button to the lock rotation setting. I changed it back to work as the mute button in the settings and voila: it's working again