The only React.js component test you'll ever need (Enzyme + Chai)

my-component.spec.js

import React from 'react';
import { shallow } from 'enzyme';
import MyComponent from '../src/my-component';

const wrapper = shallow(<MyComponent/>);

describe('(Component) MyComponent', () => {
  it('renders without exploding', () => {
    expect(wrapper).to.have.length(1);
  });
});

@michel-weber (and others ending up here) the wrapper returned by shallow is not an instance of a React component.
It is an array-like object (having a length property).

It is the same as what you get back from wrapper.find('...something...'). Which is an array of items that match your selector.
With the result of shallow this is generally only one component. But one or more doesn't matter in this case. What matters is that it isn't zero, as that lets you know rendering failed.

Also, without chai, you'd write assert(wrapper.length === 1);.

For those of us using Jest, you would check the length with expect(wrapper).toHaveLength(1)

@chiedo Does it do that? I'm not seeing where this happens.

For those in 2018 using create-react-app: https://github.com/facebook/create-react-app/blob/master/packages/react-scripts/template/README.md#testing-components

tl;dr; use:

import React from 'react';
import ReactDOM from 'react-dom';
import App from './App';

it('renders without crashing', () => {
  const div = document.createElement('div');
  ReactDOM.render(<App />, div);
});