To make up for the lack of tactile keyboard on its on-screen keyboard, the iPhone, by default, plays a clicking sound every time you tap a key. If you no longer hear this sound, there's no need to worry. All you need to do is switch it back on.
Switch off the Silence
Check the silent switch on the side of the iPhone, directly above the volume buttons. The keyboard clicks are among the sounds muted by this switch, so if you've toggled it to set your iPhone to silent, you won't be hearing any keyboard clicks. Similarly, if you've set the ringer volume all the way down, either in your iPhone's settings or using the volume buttons, the keyboard clicks will be almost or completely inaudible, as that setting affects them too.
Change Click Sounds
If your iPhone isn't on silent and the ringer volume is all the way up, the issue lies in the settings. You'd think the relevant option would be in the Keyboard section, and that's probably where you've looked. Instead, go back to the main settings screen, tap "Sounds," and then scroll to the very bottom of the screen. Switch on "Keyboard Clicks" to get the familiar clicking noise back. While you're here, you may also switch "Lock Sounds" on. When active, this latter option makes your iPhone produce a clicking sound, similar to and yet distinct from the keyboard clicks, whenever you lock it.
Information in this article applies to iPhones running iOS 7. It may vary slightly or significantly with other versions.