[trio]

выделяются сразу все, не совсем то

<input type="checkbox" id="check1">
<input type="checkbox" id="check2">
<input type="checkbox" id="check3">

(function(){
    var check = document.querySelectorAll('input');
    for (var z = 0, checkid; checkid = check[z]; z++) {
        if (localStorage[checkid.id] !== undefined) {
            checkid.checked = localStorage[checkid.id];
        }
        checkid.onchange = function() {
            localStorage[this.id] = this.checked;
        }
    }
})()