I updated your original code, added a active button variable which is chosen from the event target, this way, it doesn't matter how many buttons you want to count, they will all be unique, and you don't need a variable for each one.
This is similar to [stephen.vakil] post, however with this code, you do not need to name the buttons, just use the DOM and event target to define the uniqueness.
var count = 0;
var button1 = document.getElementById("Button1");
var button2 = document.getElementById("Button2");
var display = document.getElementById("displayCount");
var activeTarget; // which target are we counting
function clickCount(e){
var e = e || window.event; // IE or other browser event
var target = e.target || e.srcElement; // target from different browsers
if(target != activeTarget) { // Is this the current target?
count = 0; // No, reset counter
activeTarget = target; // and make it the active target
}
count++; // No matter which target, incr counter
display.innerHTML = count; // and display result
}
button1.onclick = function(e) { // don't forget the event arg
clickCount(e); // and pass it to the count function
}
button2.onclick = function(e) { // same as above
clickCount(e);
}
<input type="button" value="button1" id="Button1" />
<input type="button" value="button2" id="Button2" />
<p>Clicks: <span id="displayCount">0</span> times.</p>
The reference for the source event target onclick calling object