1930 American ad for Bifur (1928) [Daylight Fonts · Fonts In Use · Identifont].

I like this animated specimen for Warning:

And the Kablammo minisite:

Fonts have existed since the invention of the printing press in the 15th century. (Arguably longer, depending on your definition of "font".)

But until the 1800s, fonts generally weren't seen as unique designs, but as generic, interchangeable commodities. They didn't have names, and it's very difficult to tell one font from another.

Here's an example of a type specimen from 1768, where the fonts are identified by size ("English" ≈ 0.2 inches) and by founder:

Here's a couple of early examples of fonts with unique, identifiable designs, from 1805. But they still don't have names; they're both just labeled "ornamented":