I searched for a countdown timer, and I was not able to find it. It should be there in every phone... Is it coming with the standard Clock app?
Until Android 4.2 there is no stock Countdown timer, with Android 4.2 there will be one.
Some alternative Interfaces like Touchwiz (Samsung Devices) have added a Countdown Timer for a long time, but stock Android (AOSP) had this first in 4.2.
There is not a countdown app built in to android, but there are a ton to choose from on the android market.
There's definitely a built-in stopwatch for Android (HTC) 4. With my old Android 2.3, I used "Stopwatch & Countdown Timer". It seems complex, but it works well.
I have downloaded the free Kitchentimer from googleplay that is available for android 2.1 and up. It has 3 independant timers that can give an alert sound and/or vibrate after the timer has finished.