Viewers Like You

The Trope Namer is PBS, whose stations and original programs used to be funded almost entirely by viewers. (Some stations still are.) For this reason, most PBS programs still end their acknowledgements with "Made possible by ... Viewers Like You." Odds are, fewer viewers donate than not. People usually donate to PBS not because it helps keep the station running, but because neat "gifts" get thrown in (albeit for far more than the free-market rate), and because it's the PBS equivalent of Ratings: the sorts of programs that bring in heavy donations during pledge drives are the sorts of programs that the station will renew. Most of the grant money comes from airtime-hungry corporations, not-for-profit foundations, and the Corporation for Public Broadcasting ("A private corporation funded by ~~taxpayers~~ the American people").

"If you watch even one second of PBS and don't contribute, you're a thief. A common thief!"

—Betty White, The Simpsons, "Missionary: Impossible"

People who donate money directly to the producer or distributor of works, in hopes of seeing more like them.
Viewers of programs whose primary funding comes from voluntary donations, rather than advertising or subscription.

Examples of Viewers Like You include:

Web Original

Many Internet radio stations/networks, including Soma FM, mvyradio.com, and many others.
Leo Laporte's TWiT network, though in that case Leo's pay comes almost solely from viewer/listener contributions rather than advertising (more a self-move to make him accountable to those who watch), which mainly goes to technical operations and other employees.
Anybody with a Paetron link on their homepage.

Western Animation

In Justice League, The Culture Channel is used as a Brick Joke in the 2-parter "Injustice For All". The Ultra-Humanite is seen earlier in the episode enjoying an opera on the Culture Channel in prison, to Lex Luthor's displeasure. Later, when he's been paid off to betray Luthor, he donates it to the Culture Channel, leading to this hilarious parody of the line:

Announcer: The following programming was made possible by generous grants from the Ultra-Humanite and Viewers Like You.

Real Life

NPR
TBN (Trinity Broadcast Network)
Link TV (Only on Direc TV, Dish and the web)
EWTN (a Roman Catholic network, with their very odd "Religious Catalouge" program)
Most Christian television and radio, and religious media in general for that matter, with one big exception.
Canadian provincial television (TV Ontario and BC's Knowledge Network).
PBS. In 1999, a mandate was issued which requires Thanking the Viewer.