The best way to give back as a designer is by:
Helping SMALL community projects and foundations
Unlike the Unicef and other big names who aren't anyway accepting the services of non-firm based designers (they have huge budgets), small community projects and foundations do need help to raise funds and have very limited budgets. In fact, most of their members are not even paid. The other issue with big foundation is the heavy bureaucracy, concours and paperwork; there's way more freedom with small community projects and foundations even though they also have their own administrative obligations.
Whats awesome with helping foundations that don't have much budget is they let us a lot of freedom for the design and they're always appreciative of the help we give them. Plus, it's fun. From my experience, these people are easy to deal with, reasonable and cry of joy almost every time you present them the first proofs. Smaller foundations will accept any help, even though it's less "prestigious"; it's still helping a cause and it's a good opportunity to create some that looks awesome. It's also nice material to add to a portfolio.
I love working with foundations. The ones I work with help teenagers and endangered species. There's tons of them and I help them with design but also their marketing for fund raising. I don't get "anything" from this since most of them are not located in my country, but I don't care, I work for the cause, increasing my network and the fun of having freedom in the design I create.
Creating a fund raising by giving rebates to your clients in exchange of donations
I organize at least 1-2 a year a little call to action for donations for the foundations I help. I encourage my clients to donate to these foundations and in exchange I personally give a rebate to the clients on their next projects, if they donated. This is a system that works very well.
Helping beginners and being nice with them
Some young people got talent, they got passion but they don't have a mentor, direction, money for their education or someone patient enough to help them start a career.
Helping people find their way in graphic design or as illustrator is an awesome way to give back. Artistic jobs are often despised by some parents or friends as being for "brainless" only; it's good to show to some motivated and skilled person that design is something they can live from, and be proud of their skills. Most of us probably once knew that one senior designer who gave us a chance, opened their professional network to us or taught us something we still use everyday; we can now be these guys.
Who are the most memorable mentors? The ones who didn't patronize us, the ones who were respectful, the ones who didn't constantly appeal to authority, the ones who didn't consider us morons for asking beginner's questions...!
(Not downvoting the poor beginners with a big 1 point reputation because they don't know the exact rules when asking questions... but explain them what's wrong instead :)
Bringing some fun in the world
Create, create, create and make people laugh! Crazy, grotesque or clumsy Photoshop montages and 'anti-pub' are easy to do and they bring a smile on people's face. Not global enough? Wrong. I still have some of my funny montages and .wav recording done almost 20 years ago still being shared online.
That's how I donate. I don't believe much in "big prestigious donations"; I think I have more impact in small actions instead.