@model List<string>
@Html.DropDownListFor(x => x)

@model List<string>
@Html.DropDownList(
    "Foo",
    new SelectList(
        Model.Select(x => new { Value = x, Text = x }),
        "Value",
        "Text"
    )
)

<select name="Foo" id="Foo">
    <option value="item 1">item 1</option>
    <option value="item 2">item 2</option>
    <option value="item 3">item 3</option>
    ...
</select>

public class MyListModel
{
    public string SelectedItemId { get; set; }
    public IEnumerable<SelectListItem> Items { get; set; }
}

@model MyListModel
@Html.DropDownListFor(
    x => x.SelectedItemId,
    new SelectList(Model.Items, "Value", "Text")
)

List<string> ShipNames = new List<string>(){"A", "A B", "A B C"};

@Html.DropDownListFor(x => x.ShipNames, new SelectList(Model.ShipNames), "Select a Ship...", new { @style = "width:500px" })

<select id="ShipNames" name="ShipNames" style="width:500px">
    <option value="">Select a Ship...</option>
    <option>A</option>
    <option>A B</option>
    <option>A B C</option>
</select>

yourRecord.FieldName = Request.Form["FieldNameInModel"];