[css] Alternating Row Colors in Bootstrap 3 - No Table

Since you are using bootstrap and you want alternating row colors for every screen sizes you need to write separate style rules for all the screen sizes.

/* For small screen */
.row :nth-child(even){
  background-color: #dcdcdc;
}
.row :nth-child(odd){
  background-color: #aaaaaa;
}

/* For medium screen */    
@media (min-width: 768px) {
    .row :nth-child(4n), .row :nth-child(4n-1) {
        background: #dcdcdc;
    }
    .row :nth-child(4n-2), .row :nth-child(4n-3) {
        background: #aaaaaa;
    }
}

/* For large screen */
@media (min-width: 992px) {
    .row :nth-child(6n), .row :nth-child(6n-1), .row :nth-child(6n-2) {
        background: #dcdcdc;
    }
    .row :nth-child(6n-3), .row :nth-child(6n-4), .row :nth-child(6n-5) {
        background: #aaaaaa;
    }
}

Working FIDDLE
I have also included the bootstrap CSS here.