can jqgrid support dropdowns in the toolbar filter fields

There are some common rules for all types of sorting in jqGrid

{
    name: 'Category', index: 'Category', width: 200, formatter:'select', 
    stype: 'select', searchoptions:{ sopt:['eq'], value: categoriesStr }
}

where categoriesStr are defined as

var categoriesStr = ":All;1:sport;2:science";

Here additionally to the standard “1:sport;2:science” values are inserted “:All” string which allow you don’t filter the the column. You can of course use “:” or “:Select…” and so on.

On the demo prepared for the answer you can see the close results.

UPDATED: I find your question interesting and made the demo. It shows how one can build the select comboboxes which can be used in the search toolbar or in the advanced searching dialog based on the text contain of the corresponding column. For one column I use additionally jQuery UI autocomplete. You can modify the code to use more different powerful options of the autocomplete. Here is the code of the code:

var mydata = [
        {id:"1", Name:"Miroslav Klose",     Category:"sport",   Subcategory:"football"},
        {id:"2", Name:"Michael Schumacher", Category:"sport",   Subcategory:"formula 1"},
        {id:"3", Name:"Albert Einstein",    Category:"science", Subcategory:"physics"},
        {id:"4", Name:"Blaise Pascal",      Category:"science", Subcategory:"mathematics"}
    ],
    grid = $("#list"),
    getUniqueNames = function(columnName) {
        var texts = grid.jqGrid('getCol',columnName), uniqueTexts = [],
            textsLength = texts.length, text, textsMap = {}, i;
        for (i=0;i<textsLength;i++) {
            text = texts[i];
            if (text !== undefined && textsMap[text] === undefined) {
                // to test whether the texts is unique we place it in the map.
                textsMap[text] = true;
                uniqueTexts.push(text);
            }
        }
        return uniqueTexts;
    },
    buildSearchSelect = function(uniqueNames) {
        var values=":All";
        $.each (uniqueNames, function() {
            values += ";" + this + ":" + this;
        });
        return values;
    },
    setSearchSelect = function(columnName) {
        grid.jqGrid('setColProp', columnName,
                    {
                        stype: 'select',
                        searchoptions: {
                            value:buildSearchSelect(getUniqueNames(columnName)),
                            sopt:['eq']
                        }
                    }
        );
    };

grid.jqGrid({
    data: mydata,
    datatype: 'local',
    colModel: [
        { name:'Name', index:'Name', width:200 },
        { name:'Category', index:'Category', width:200 },
        { name:'Subcategory', index:'Subcategory', width:200 }
    ],
    sortname: 'Name',
    viewrecords: true,
    rownumbers: true,
    sortorder: "desc",
    ignoreCase: true,
    pager: '#pager',
    height: "auto",
    caption: "How to use filterToolbar better locally"
}).jqGrid('navGrid','#pager',
          {edit:false, add:false, del:false, search:false, refresh:false});

setSearchSelect('Category');
setSearchSelect('Subcategory');

grid.jqGrid('setColProp', 'Name',
            {
                searchoptions: {
                    sopt:['cn'],
                    dataInit: function(elem) {
                        $(elem).autocomplete({
                            source:getUniqueNames('Name'),
                            delay:0,
                            minLength:0
                        });
                    }
                }
            });

grid.jqGrid('filterToolbar',
            {stringResult:true, searchOnEnter:true, defaultSearch:"cn"});

Is this what you want?

UPDATED: One more option could be the usage of select2 plugin which combines the advantages of dropdown and comfortable searching by Autocomplete. See the answer and this one (see the demo) for demos (this one and this one) and code examples.

UPDATED 2: The answer contains the modification of above code to work with jqGrid 4.6/4.7 or with free jqGrid 4.8.