Magento 2.1 – Hide and Show Field Based on Dropdown Selection

Try this (Note: Don't forget to replace the line "Namespace" and the line "ModuleName" with your values):

<field name="field1">
    <argument name="data" xsi:type="array">
        <item name="options" xsi:type="object">Namespace\ModuleName\Model\Config\Source\Options</item>
        <item name="config" xsi:type="array">
            <item name="label" xsi:type="string" translate="true">Parent Option</item>
            <item name="component" xsi:type="string">Namespace_ModuleName/js/form/element/options</item>
            <item name="visible" xsi:type="boolean">true</item>
            <item name="dataType" xsi:type="string">number</item>
            <item name="formElement" xsi:type="string">select</item>
            <item name="source" xsi:type="string">item</item>
            <item name="dataScope" xsi:type="string">field1</item>
            <item name="sortOrder" xsi:type="number">210</item>
            <item name="validation" xsi:type="array">
                <item name="required-entry" xsi:type="boolean">true</item>
            </item>
        </item>
    </argument>
</field>

<field name="field2Depend1">
    <argument name="data" xsi:type="array">
        <item name="config" xsi:type="array">
            <item name="label" xsi:type="string">Field 1</item>
            <item name="dataType" xsi:type="string">text</item>
            <item name="formElement" xsi:type="string">input</item>
            <item name="source" xsi:type="string">item</item>
            <item name="sortOrder" xsi:type="number">220</item>
            <item name="breakLine" xsi:type="boolean">true</item>
            <item name="visibleValue" xsi:type="string">2</item>
            <item name="visible" xsi:type="boolean">false</item>
        </item>
    </argument>
</field>
<field name="field3Depend1">
    <argument name="data" xsi:type="array">
        <item name="config" xsi:type="array">
            <item name="label" xsi:type="string">Field 2</item>
            <item name="dataType" xsi:type="string">text</item>
            <item name="formElement" xsi:type="string">input</item>
            <item name="source" xsi:type="string">item</item>
            <item name="sortOrder" xsi:type="number">230</item>
            <item name="breakLine" xsi:type="boolean">true</item>
            <item name="visibleValue" xsi:type="string">0</item>
            <item name="visible" xsi:type="boolean">false</item>
        </item>
    </argument>
</field>

Where:

• The child elements visibility is set by default as false;
• The visibleValue - is field1 value when element should be visible;

Namespace\ModuleName\Model\Config\Source\Options

namespace Namespace\ModuleName\Model\Config\Source;

use Magento\Framework\Option\ArrayInterface;

class Options implements ArrayInterface
{
    /**
     * @return array
     */
    public function toOptionArray()
    {
        $options = [
            0 => [
                'label' => 'Please select',
                'value' => 0
            ],
            1 => [
                'label' => 'Option 1',
                'value' => 1
            ],
            2  => [
                'label' => 'Option 2',
                'value' => 2
            ],
            3 => [
                'label' => 'Option 3',
                'value' => 3
            ],
        ];

        return $options;
    }
}

app/code/Namespace/ModuleName/view/adminhtml/web/js/form/element/options.js

define([
    'underscore',
    'uiRegistry',
    'Magento_Ui/js/form/element/select',
    'Magento_Ui/js/modal/modal'
], function (_, uiRegistry, select, modal) {
    'use strict';

    return select.extend({

        /**
         * On value change handler.
         *
         * @param {String} value
         */
        onUpdate: function (value) {
            console.log('Selected Value: ' + value);

            var field1 = uiRegistry.get('index = field2Depend1');
            if (field1.visibleValue == value) {
                field1.show();
            } else {
                field1.hide();
            }

            var field2 = uiRegistry.get('index = field3Depend1');
            if (field2.visibleValue == value) {
                field2.show();
            } else {
                field2.hide();
            }

            return this._super();
        },
    });
});

Result:

Value 0 selected:

Value 1 selected:

Value 2 selected:

Value 3 selected:

PS: Possibly it not the best solution, but it shall help you

First set:

<item name="disabled" xsi:type="string">${ $.provider }:data.do_we_hide_it</item>

Suppose Vendor\Extension\Model\Notification\DataProvider is your data provider for UI:

<dataSource name="notification_edit_data_source">
    <argument name="dataProvider" xsi:type="configurableObject">
        <argument name="class" xsi:type="string">Vendor\Extension\Model\Notification\DataProvider</argument>
        <argument name="name" xsi:type="string">notification_edit_data_source</argument>

Then in its getData function add the following lines:

public function getData(){
.....
.....
if(condition1)
    $this->loadedData[$entity_id]['do_we_hide_it'] = true;
else
    $this->loadedData[$entity_id]['do_we_hide_it'] = false;

See the core files vendor/magento/module-catalog/view/adminhtml/ui_component/category_form.xml line 377 and vendor/magento/module-catalog/Model/Category/DataProvider.php line 303 for an example.