Пример на jsfiddle https://jsfiddle.net/al_n_user/1fmwhuse/3/

<ul id="block_list1">
                <li class="list1">203-810-4300</li>
                <li class="list2">203-810-4333</li>
                <li class="list3">Contact@lpsum.com</li>
                <li class="list4">50 W ashingto street</li>
                <li class="list5">Sute 1048</li>
                <li class="list6">lispume 0644</li>
            </ul>

#block_list1 li {
    margin: 20px 0 0 20px;
    padding: 3px 0 3px 3px;
    color:#fff;
    background-color: #000;
    font: 15px Verdana;
    width: 140px;
}
#block_list1 .list1 {
    list-style-image: url(../images/imgPhone.jpg);
    height: 20px; /*когда пытаюсь выравнять блок с текстом*/
}

#block_list1 .list2 {
    list-style-image: url(../images/imgFax.jpg);
}

#block_list1 .list3 {
    list-style-image: url(../images/imgMail.jpg);
    margin: 30px 0 0 20px;
    width: 190px;
}

#block_list1 .list4 {
    list-style-image: url(../images/imgStreet.jpg);
    margin: 30px 0 0 20px;
    width: 165px;
}

#block_list1 .list5 {
    margin: 2px 0 0 20px;
    width: 90px;
}

#block_list1 .list6 {
    margin: 2px 0 0 20px;
    width: 150px;
}