I do, for example, in the case of supporting online content producers (see e.g. Patreon). They're not technically charities or nonprofits, but I am giving away my money for nothing, so it's kinda like charity. I do so because I want to provide incentives for them to keep doing the work they do.
It is, I suppose, a bit like donating to GiveWell or any of the other meta-charities. By GiveWell's own standards, it is technically speaking not a top charity, but it still does work that I believe matters a lot, even if its benefits are not easily measurable.
Self-promotion: New YouTube video on effective altruism. Please take a look and share if you think it is any good. "The Price of Saving a Life ... is $3,340." https://www.youtube.com/watch?v=2tAaO5KmRFQ&index=2&list=PL0FfKwFuQb2T5tGSKh254JleBGyydQDUR
Looks good I'll check it out.
I think social media and YouTube videos are the best way to mass communicate these days.
I don't have any good ideas, but I think "Doing Good Effectively By Using Reason" is a bit too wordy and clunky for a T-shirt slogan.