I'm a beginner in web application development and I'm wondering if there are places to find smaller projects to practice one's skills. The reason I'm asking this is because where I'm from there used to be, though quite a few years ago, a website for freelancing where you initially took simpler tasks that didn't pay you in order to get "reputation" on the website so people would trust you with more sophisticated tasks. Even though I find the system itself questionable I wonder if there is anything similar on a more global scale that would allow me to practice my skills on simple apps.
My question is why? If you look around, you'll see others recommending how to get your foot in the door.
If you want to practice a skill, you need to sometimes create the project to practice it on. Create a fictitious company (Example Corp), and design your Web App around their requirements. Then, once you have a working product, put it in your portfolio.
What if you're not creative enough to design for Example Corp? How can I get my name out there locally?
Try talking to non-profit organizations in your area. Most will accept people creating value for them for free, and will even be a great reference! Use this to get practice dealing with an organization (of any size), take note of what works and doesn't, then continue from there.
Once you get your portfolio setup, you can spend more time designing / building, and less time haggling.