In Scene Title Text

Not really painted on, but it sure looks like it.

In the early days of TV the best way to display text to your viewers was to put a physical card in front of the camera with that text on it, hence the name Episode Title Card. Advances in production meant that later that text could be edited directly into the film rather than having a physical card, and further advances meant that you could even display the text on the screen overtop of a normal scene (an 'overlay'). The overlay text will act like it's stuck to the screen though—it won't move on the screen even if the camera angle changes.

Nowadays the latest CGI will let you make it seem like overlay text is physically in the scene again. It can look like it's written on a highway overpass, or floating on the surface of the water. It is perspective corrected to seem as if it's in the scene, will move when the camera (or the object it's written on) moves, and might even be lit as if it were in the scene. However characters do not notice or acknowledge it and the audience is expected to understand that the text doesn't actually exist in the scene, it's just a novel way of displaying it. This can also be done with a Title In or any other text presented to the audience.

Examples of In Scene Title Text include:

Film

The Watchmen movie plays with this in the title credits, including having characters appear to react to the text as it flies over their heads (only for it to reveal they were reacting to fighter jets flying just behind the text) as well as having the text reflect off an astronaut's visor.
The rules in Zombieland appear in this fashion.
The opening credits of Moon.
Used often in Stranger Than Fiction to represent the protagonist's OCD.
The opening credits of Cats Don't Dance.
Played with in Johnny Dangerously. The opening scene has a subtitle reading "1935"... which is then run over by a car.
The opening credits to Star Wars could be considered an example of this, since they're perspective-corrected and disappear into space.
Used for the opening credits of David Fincher's Panic Room. Explicitly said to be the inspiration for Fringe's 3-D titles, as per Word of God.

Live action TV

The Episode Title Card for Heroes is very frequently done this way. See the gallery here and a Vimeo tutorial here.
Fringe also does this frequently.
The intro theme for The Chicago Code uses this for the main title card, but not the intro credits. (This video at 0:27)
There's an HBO advertisement that they put at the beginning of their DVDs that edits show titles into clips from the show in this fashion. Used to great effect, as characters will seem to interact with the letters, even though the original scene featured no in-scene text/titles.
Used in the new re-envisioning of Sherlock for text messages and other text otherwise unseen by the audience.
Green Acres often played with how the opening credits were shown. Sometimes the credits were printed on objects like newspapers or eggs, and sometimes characters were aware of their presence, commenting on those names that seem to appear out of nowhere.
Played for laughs in Milton Jones's House of Rooms. The title appears at the bottom of the screen before being carried away by a garbageman. After the break, the gag is repeated - but this time the title is not part of the scene, and his hand passes through it.

Video Games

The introductory cutscene to Borderlands has this.
Mirror's Edge has this in its opening scene as well.

Western Animation

Scooby-Doo and the Ghoul School plays with this trope. At the beginning of the telefilm, after the title appears over a stormy night sky, Scooby points upward and says, "Look, Shaggy … writing!" Naturally, Shaggy thinks Scooby said "lightning".
Older Than They Think: Many Looney Tunes shorts, such as "Wabbit Twouble", have the opening credits as part of the scene.