How add Custom Validation Rules when using Form Request Validation in Laravel 5

Using Validator::extend() like you do is actually perfectly fine you just need to put that in a Service Provider like this:

<?php namespace App\Providers;

use Illuminate\Support\ServiceProvider;

class ValidatorServiceProvider extends ServiceProvider {

    public function boot()
    {
        $this->app['validator']->extend('numericarray', function ($attribute, $value, $parameters)
        {
            foreach ($value as $v) {
                if (!is_int($v)) {
                    return false;
                }
            }
            return true;
        });
    }

    public function register()
    {
        //
    }
}

Then register the provider by adding it to the list in config/app.php:

'providers' => [
    // Other Service Providers

    'App\Providers\ValidatorServiceProvider',
],

You now can use the numericarray validation rule everywhere you want

While the above answer is correct, in a lot of cases you might want to create a custom validation only for a certain form request. You can leverage laravel FormRequest and use dependency injection to extend the validation factory. I think this solution is much simpler than creating a service provider.

Here is how it can be done.

use Illuminate\Validation\Factory as ValidationFactory;

class UpdateMyUserRequest extends FormRequest {

    public function __construct(ValidationFactory $validationFactory)
    {

        $validationFactory->extend(
            'foo',
            function ($attribute, $value, $parameters) {
                return 'foo' === $value;
            },
            'Sorry, it failed foo validation!'
        );

    }

    public function rules()
    {
        return [
            'username' => 'foo',
        ];
    }
}

The accepted answer works for global validation rules, but many times you will be validating certain conditions that are very specific to a form. Here's what I recommend in those circumstances (that seems to be somewhat intended from Laravel source code at line 75 of FormRequest.php):

Add a validator method to the parent Request your requests will extend:

<?php namespace App\Http\Requests;

use Illuminate\Foundation\Http\FormRequest;
use Validator;

abstract class Request extends FormRequest {

    public function validator(){

        $v = Validator::make($this->input(), $this->rules(), $this->messages(), $this->attributes());

        if(method_exists($this, 'moreValidation')){
            $this->moreValidation($v);
        }

        return $v;
    }
}

Now all your specific requests will look like this:

<?php namespace App\Http\Requests;

use App\Http\Requests\Request;

class ShipRequest extends Request {

    public function rules()
    {
        return [
            'shipping_country' => 'max:60',
            'items' => 'array'
        ];
    }

    // Here we can do more with the validation instance...
    public function moreValidation($validator){

        // Use an "after validation hook" (see laravel docs)
        $validator->after(function($validator)
        {
            // Check to see if valid numeric array
            foreach ($this->input('items') as $item) {
                if (!is_int($item)) {
                    $validator->errors()->add('items', 'Items should all be numeric');
                    break;
                }
            }
        });
    }

    // Bonus: I also like to take care of any custom messages here
    public function messages(){
        return [
            'shipping_country.max' => 'Whoa! Easy there on shipping char. count!'
        ];
    }
}