Edit in JSFiddle

function Select($el) {
    this.$el = $($el);
    this.$select = this.$el.find('.select-select');
    this.select = this.$select[0];
    this.$value = this.$el.find('.select-value');

    this.$select.on('change keydown', $.proxy(this, '_onChange')).change();
}

Select.prototype._onChange = function (e) {
    setTimeout($.proxy(this, 'update'), 0);
};

Select.prototype.update = function () {
    var option = this.select.options[this.select.selectedIndex];
    var value = option.textContent || options.innerText;
    this.$value.text(value);
};


$(function () {
    $('.select').each(function () {
        new Select(this);
    });
});

<h3>基本形</h3>
<p>
    <span class="select">
        <select class="select-select">
            <option>1 ほげほげ</option>
            <option>2 ふがふがふがふがふがふが</option>
            <option>3 ぴよ</option>
        </select>
        <span class="select-value"></span>
    </span>
</p>

<h3>max-width を当てる</h3>
<p>
    <span class="select" style="max-width:300px">
        <select class="select-select">
            <option>ほげほげ</option>
            <option>ふがふがふがふがふがふがふがふがふがふがふがふが</option>
            <option>ぴよ</option>
        </select>
        <span class="select-value"></span>
    </span>
</p>

<h3>テキストと並べる</h3>
<p>
    ほげほげ
    <span class="select" style="max-width:300px">
        <select class="select-select">
            <option>ほげ</option>
            <option>ふが</option>
            <option>ぴよ</option>
        </select>
        <span class="select-value"></span>
    </span>
    ふがふが
</p>

<h3>ちょっとカッコよくする</h3>
<p>
    <span class="select select_cool">
        <select class="select-select">
            <option>1 ほげほげ</option>
            <option>2 ふがふがふがふがふがふが</option>
            <option>3 ぴよ</option>
        </select>
        <span class="select-value"></span>
    </span>
</p>

html {
    background-color: #eee;
}

.select {
    display: inline-block;
    position: relative;
    z-index: 0;
    border: 3px solid #000;
    overflow: hidden;
}

.select:after {
    content: "▼";
    display: block;
    position: absolute;
    top: 0;
    right: 0;
    width: 20px;
    color: #fff;
    background-color: #000;
    text-align: center;
    line-height: 28px;
}

.select-select {
    position: relative;
    z-index: 2;
    width: 100%;
    height: 28px;
    margin: 0;
    padding: 3px 30px 3px 3px;
    font: inherit;
    opacity: 0;
    -ms-filter: alpha(opacity=0);
    -webkit-appearance: none;
}

.select-select:focus {
    filter: none;
}

.select-value {
    -moz-box-sizing: border-box;
    box-sizing: border-box;
    position: absolute;
    top: 0;
    right: 0;
    bottom: 0;
    left: 0;
    z-index: 1;
    overflow: hidden;
    width: auto;
    height: auto;
    padding: 0 20px 0 9px;
    line-height: 28px;
    white-space: nowrap;
    text-overflow: ellipsis;
}

.select-select:focus ~ .select-value {
    outline: thin dotted #333;
    outline: 2px auto -webkit-focus-ring-color;
    outline-offset: -2px;
}

.select_cool {
    background: url(http://necomesi.jp/blog/tsmd/wp-content/uploads/sites/3/2014/04/select_bg.png) no-repeat right center #fff;
    border: 1px solid #ccc;
    border-radius: 3px;
    box-shadow: 1px 1px 0 rgba(255, 255, 255, .5);
}

.select_cool:after {
    content: normal;
}