Finding matching objects in an array of objects?

Using arrow functions with an implied return and concise body:

const results = set.filter(entry => entry.color === "green");

Another example passing in a search variable:

const searchString = 'green'; 
const results = set.filter(entry => entry.color === `${searchString}`);

Read more about arrow functions on MDN

Using Array#filter, for this particular case the code would look like

var results = set.filter(function (entry) { return entry.color === "green"; });

Array#filter is not implemented in some older browsers, so see the linked article for a backward compatibility shim, or better yet get a full-fledged ES5 shim.

For the more general case, it's just a matter of extending this idea:

function findByMatchingProperties(set, properties) {
    return set.filter(function (entry) {
        return Object.keys(properties).every(function (key) {
            return entry[key] === properties[key];
        });
    });
}

var results = findByMatchingProperties(set, { color: "green" });

Again, I am using ECMAScript 5 methods Object.keys and Array#every, so use an ES5 shim. (The code is doable without an ES5 shim but uses manual loops and is much less fun to write and read.)

I have used map function from jquery and I am getting selected index by passing searched key value so by using that index we will get required object from array.

var mydata = [{ name: "Ram", Id: 1 }, { name: "Shyam", Id: 2 }, { name: "Akhil", Id: 3 }];

searchKey = 2

var mydata = [{ name: "Ram", Id: 1 }, { name: "Shyam", Id: 2 }, { name: "Akhil", Id: 3 }];

searchKey = 2

var selectedData = mydata[mydata.map(function (item) { return item.Id; }).indexOf(searchKey)];

console.log(selectedData)

var selectedData = mydata[mydata.map(function (item) { return item.Id; }).indexOf(searchKey)];

console.log(selectedData)

output
{ name: "Shyam", Id: 2 }

Note: if you want to pass search key as object then
searchKey = { Id: 2 };

mydata[mydata.map(function (item) { return item.Id; }).indexOf(searchKey.Id)];

output
{ name: "Shyam", Id: 2 }

Since you've included the jQuery tag, here's one way to do it using jQuery's map:

var results = $.map( set, function(e,i){
  if( e.color === 'green' ) return e; 
});

The documentation states that you need to return null to remove the element from the array, but apparently this is false, as shown by the jsFiddle in the comments; returning nothing (i.e. returning undefined) works just as well.