Idiomatically find the number of occurrences a given value has in an array

reduce is more appropriate here than filter as it doesn't build a temporary array just for counting.

var dataset = [2,2,4,2,6,4,7,8];
var search = 2;

var count = dataset.reduce(function(n, val) {
    return n + (val === search);
}, 0);

console.log(count);

In ES6:

let count = dataset.reduce((n, x) => n + (x === search), 0);

Note that it's easy to extend that to use a custom matching predicate, for example, to count objects that have a specific property:

people = [
    {name: 'Mary', gender: 'girl'},
    {name: 'Paul', gender: 'boy'},
    {name: 'John', gender: 'boy'},
    {name: 'Lisa', gender: 'girl'},
    {name: 'Bill', gender: 'boy'},
    {name: 'Maklatura', gender: 'girl'}
]

var numBoys = people.reduce(function (n, person) {
    return n + (person.gender == 'boy');
}, 0);

console.log(numBoys);

Counting all items, that is, making an object like {x:count of xs} is complicated in javascript, because object keys can only be strings, so you can't reliably count an array with mixed types. Still, the following simple solution will work well in most cases:

count = function (ary, classifier) {
    classifier = classifier || String;
    return ary.reduce(function (counter, item) {
        var p = classifier(item);
        counter[p] = counter.hasOwnProperty(p) ? counter[p] + 1 : 1;
        return counter;
    }, {})
};

people = [
    {name: 'Mary', gender: 'girl'},
    {name: 'Paul', gender: 'boy'},
    {name: 'John', gender: 'boy'},
    {name: 'Lisa', gender: 'girl'},
    {name: 'Bill', gender: 'boy'},
    {name: 'Maklatura', gender: 'girl'}
];

// If you don't provide a `classifier` this simply counts different elements:

cc = count([1, 2, 2, 2, 3, 1]);
console.log(cc);

// With a `classifier` you can group elements by specific property:

countByGender = count(people, function (item) {
    return item.gender
});
console.log(countByGender);

2017 update

In ES6, you use the Map object to reliably count objects of arbitrary types.

class Counter extends Map {
    constructor(iter, key=null) {
        super();
        this.key = key || (x => x);
        for (let x of iter) {
            this.add(x);
        }
    }
    add(x) {
      x = this.key(x);
      this.set(x, (this.get(x) || 0) + 1);
    }
}

// again, with no classifier just count distinct elements

results = new Counter([1, 2, 3, 1, 2, 3, 1, 2, 2]);
for (let [number, times] of results.entries())
    console.log('%s occurs %s times', number, times);


// counting objects

people = [
    {name: 'Mary', gender: 'girl'},
    {name: 'John', gender: 'boy'},
    {name: 'Lisa', gender: 'girl'},
    {name: 'Bill', gender: 'boy'},
    {name: 'Maklatura', gender: 'girl'}
];


chessChampions = {
    2010: people[0],
    2012: people[0],
    2013: people[2],
    2014: people[0],
    2015: people[2],
};

results = new Counter(Object.values(chessChampions));
for (let [person, times] of results.entries())
    console.log('%s won %s times', person.name, times);

// you can also provide a classifier as in the above

byGender = new Counter(people, x => x.gender);
for (let g of ['boy', 'girl'])
   console.log("there are %s %ss", byGender.get(g), g);

A type-aware implementation of Counter can look like this (Typescript):

type CounterKey = string | boolean | number;

interface CounterKeyFunc<T> {
    (item: T): CounterKey;
}

class Counter<T> extends Map<CounterKey, number> {
    key: CounterKeyFunc<T>;

    constructor(items: Iterable<T>, key: CounterKeyFunc<T>) {
        super();
        this.key = key;
        for (let it of items) {
            this.add(it);
        }
    }

    add(it: T) {
        let k = this.key(it);
        this.set(k, (this.get(k) || 0) + 1);
    }
}

// example:

interface Person {
    name: string;
    gender: string;
}


let people: Person[] = [
    {name: 'Mary', gender: 'girl'},
    {name: 'John', gender: 'boy'},
    {name: 'Lisa', gender: 'girl'},
    {name: 'Bill', gender: 'boy'},
    {name: 'Maklatura', gender: 'girl'}
];


let byGender = new Counter(people, (p: Person) => p.gender);

for (let g of ['boy', 'girl'])
    console.log("there are %s %ss", byGender.get(g), g);

array.filter(c => c === searchvalue).length;

Here is one way to show ALL counts at once:

var dataset = [2, 2, 4, 2, 6, 4, 7, 8];
var counts = {}, i, value;
for (i = 0; i < dataset.length; i++) {
    value = dataset[i];
    if (typeof counts[value] === "undefined") {
        counts[value] = 1;
    } else {
        counts[value]++;
    }
}
console.log(counts);
// Object {
//    2: 3,
//    4: 2,
//    6: 1,
//    7: 1,
//    8: 1
//}

Newer browsers only due to using Array.filter

var dataset = [2,2,4,2,6,4,7,8];
var search = 2;
var occurrences = dataset.filter(function(val) {
    return val === search;
}).length;
console.log(occurrences); // 3