A free place to practice some scenarios like testing a large complicated page, working with simple HTML elements like buttons, filling out forms and automating an application that evolves over time.
Another free website that I got from a book I read called Selenium Design Patterns. This website is a simulator of an online store where you can purchase different kinds of items. You can try to automate items such as slow AJAX, slow animation, third party links, credit card transactions, and online store checkout scenarios.
Dave designed an excellent place to practice different kinds of test automation scenarios. Some of the scenarios that you can try to automate include A/B Testing, basic Auth, file Upload, challenging DOM, iFrames, slow connections, dynamic content, hovers, and redirect links.
This is an excellent demo travel site that you can use to practice your test automation. They have a front end and a back end for you to automate. This one is a bit more fancy than the website that you will see below.
This is really a nice fake e-commerce site to practice test automation. If you have a project where you need to practice different flows for online stores, this is the website you want. You can practice adding items to the cart, checking out, and validating that items have been added.
This is an app that I recently learned about from one of my coworkers. This is a sample Address Book app. Some things that you can practice here are basic CRUD operations for addresses.