I've never really understood these types of questions, but they seem to come up often enough in development and design. To me it's a very bad sign when a programmer can't think of programming projects for himself and when a designer isn't inspired to come up with projects of his own in his free time.
After all, graphic design is a field with lots of hobbyists. It's something that lots of people enjoy and are deeply passionate about. And most professionals are people who began doing art and graphic design for fun, found that they could actually make money from their hobby, and then eventually decided this was what they wanted to do for a living.
As such, it's a pretty competitive (and relatively saturated) industry. And if you don't enjoy design, you won't be inclined to practice as much, so you're gonna have a hard time competing against the legions of designers out there who live and breathe design.
It's good that you're focusing on improving rather than making money, but why do you need random strangers to make requests for you to practice with? Does a student painter or sketch artist need requests from strangers in order to practice their art? If you were learning math, would you look for strangers to give you math problems to perform?
Sure, you should be open to requests and accept the extra practice, but a random stranger's graphic design request won't help you develop your aesthetic eye or technical skills any more than personal projects you came up with yourself. If anything, your own personal projects will give you more freedom to express yourself, and designing when you're actually inspired will produce better results (largely because it's more enjoyable, which also motivates you to push yourself harder).
That said, there is
value in taking an academic approach and getting professional guidance. Receiving design assignments from a design instructor does have value, as they're following a structured lesson plan
that's deisgned to give you a comprehensive and balanced look at the field of design.
Similarly, there are workbooks and other resources out there with practice design briefs. These are excellent practice projects since they're either real-life briefs used by professional agencies or created by experienced designers to provide realistic requirements you might find in a professional setting.
But a stranger on a forum who wants a banner for his site or "loading screen for his mobile game" is not a good source of design projects. Besides their not being things you'd want in your portfolio, most of these people don't know the first thing about professional design (hence why they're asking random strangers on the web to design them things for free) so their requirements and specifications won't be realistic to professional design scenarios, and this sort of practice will not teach you professional workflows. If anything, they'll just teach you bad habits.
Now, if you're really having a hard time coming up with enough personal projects to occupy yourself in your free time, you could always:
- Take a design course at a local college.
- Get an internship at a design studio or a company's design department.
- Volunteer your services to open source projects, non-profits, and public organizations (schools, libraries, or government agencies).
- Provide free design services to indie artists/musicians and filmmakers.
- Collaborate with a developer and exchange services.
- Participate in design contests.
I personally have no problem with novice designers doing work for free. If you're not competent enough to provide professional-level work, then you shouldn't really be charging anyone for it. Likewise, if you can add a really high profile project/client to your portfolio, then it may very well be worth it to do the work for a discounted rate or even for free.
If you don't have a strong portfolio, volunteer work is often the best way to get your foot in the door and start building a professional portfolio. But don't waste time designing forum signatures or a gaming clan website for some high school student on IRC. Instead, focus on getting real projects that: a.) add weight to your portfolio, or b.) contributes something positive to society, e.g. saving a nonprofit, social enterprise, or your local school district money on web design.