Before I start working with real-time sprite movement and timers, I decided to try something turn-based. So I programmed a simple set of functions to draw ASCII characters to the screen and am building a roguelike engine. But the main problem I keep running into is getting keyboard input. I can collect it just fine, the problem is that it's collected way too fast. Even tapping the key as lightly as possible detects two events at once! Is there a simple way to delay detection of key events?

Current game loop (The Draw functions near the bottom blit ASCII characters to the screen):

[EDIT]
Didn't see that the OP was using Allegro 5.

You confused me. Without scrolling down to see the rest of your code I thought you were using Allegro 4 because you are checking if (key[KEY_DOWN]) {/*...*/}. Now that I look further down, you are using Allegro 5 and are trying to emulate A4 with it. My keyboard_handler is for Allegro 4 only at this point.

So now, my advice is to drop use of your key array, and simply use the key press and release events that Allegro 5 provides for you. Ie... move the code for if (key[KEY_*]) {DoStuff();} into

else if(ev.type == ALLEGRO_EVENT_KEY_DOWN)
{
         switch(ev.keyboard.keycode) {
            case ALLEGRO_KEY_UP:
//               key[KEY_UP] = true;
               DoStuff();
               break;

The problem is that an entry from your key array will be true for several logic loops at a time. It takes at least a certain amount of time between key press and key release.

What input tutorial? What's the link to it?

There aren't any separate events for those, you'll have to track the state yourself. If you got a key down event, but haven't received a key up event then you have a key hold. For double clicks, you'll have to track the time of the last key down event and compare it to the time of the new key down event that matches it.

The code there is really only for really basic input needs. Something that only needs to know if a key is pressed at any given time. Trying to show something more complex would probably just confuse things more.

I'm open to a second Keyboard tutorial showing more advanced concepts though.

Not really. The keystate stuff is a dirty hack, imo worse than storing your own key array. Also its far less efficient. The tutorial only stores keys it needs, where as the keystate stuff stores all of them regardless. and copies them...