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
I don't think that you are totally understanding what King Penguin has posted. The volume rocker on the side of the iPad does control the volume. The side switch can mute system sounds and games use system sounds whereas music that you can play in the music app - or in videos - are not part of system sounds.
See if this makes any more sense to you - or if it is a little clearer for you to understand.
If you lose sounds for keyboard clicks, games or other apps, email notifications and other notifications, system sounds may have been muted.
System sounds can be muted and controlled two different ways. The screen lock rotation can be controlled in the same manner as well.
Settings>General>Use Side Switch to: Mute System sounds. If this option is selected, the switch on the side of the iPad above the volume rocker will mute system sounds.
If you choose Lock Screen Rotation, then the switch locks the screen. If the screen is locked, you will see a lock icon in the upper right corner next to the battery indicator gauge.
If you have the side switch set to lock screen rotation then the system sound control is in the task bar. Double tap the home button and in the task bar at the bottom, swipe all the way to the right. The speaker icon is all the way to the left. Tap on it and system sounds will return.
If you have the side switch set to mute system sounds, then the screen lock rotation can be accessed via the task bar in the same manner as described above.
This support article from Apple explains how the side switch works.
This seems like a bug to me.
I had the same issue...no sound on games, but sound on iTunes, videos, etc. But I had the rocker switch set to "lock Rotate", and it was OFF. I even got the notification at times to increase sound effects, and it allowed me to turn up the volume of sound effects. But still no game sounds.
So in the mode of "try everything" I follow the advice here: Switch the side switch to "Mute", turn it on, turn it off, and back to lock "rotate" (still off, though.) Now the sound in games works.
Anyway, it works now. But seems like a bug that would be nice to have fixed.