Currently, you can stream Shrek 2 with Netflix and The Roku Channel. You can also rent or buy Shrek 2 to watch online with iTunes, Prime Video, and Microsoft Store. We'll update this page if we find more streaming options for the movie.
Sadly you can no longer try Netflix for free, meaning you can no longer watch Shrek 2 during a free trial with Netflix. But the basic plan starts at $9.99 per month so it isn't too expensive.
We don't often recommend The Roku Channel, but it is a great stream service that is totally free. You can stream Shrek 2 via The Roku Chanel here.