Pastel-Chalked Freeze-Frame

"Oh no! The animation budget ran out!"

—Tristan Taylor, Yu-Gi-Oh!: The Abridged Series

Rather than animating a critical moment in a battle, and perhaps giving away a plot point too soon, some animators cut to or dissolve into a still image designed to look like an action shot, often blurry with motion, that shows the important hit, or dodge, or other action, without revealing anything crucial. The most attractive of these appear to be done in pastel chalks, although simple black line-drawings are also used. The Ken Burns Effect is frequently employed. These are also frequently used to emphasize especially dramatic moments, especially during cliffhangers.

This technique was invented by the late, great (and friggin' obscure) anime director Osamu Dezaki.

These kind of scenes tend to double as Freeze Frame Endings.

Examples of Pastel-Chalked Freeze-Frame include:

Anime & Manga

Classic anime director Osamu Dezaki is responsible for the popularity of these, which he termed "Postcard Memories". An example of this would be Space Adventure Cobra, where he had every commercial break and final frame fade into a beautiful pastel drawing.
Likewise, he animated the 90-minute retelling of Aim for The Ace with chalk frames on the dramatic moments. The animation was much better than the series' own.
A lot of the kendo matches in Bamboo Blade end with these; the last shot of the ED is also a Freeze Frame (of Tama-chan, natch.)
Steel Angel Kurumi is rife with these.
So is Simoun.
Pastel freeze-frames can also be found for romantic moments, usually at the end of episodes. There are a number of these in the later seasons of Ranma ½.
Yu Yu Hakusho likes to end on these. Parodied/Lampshaded in the last season, where an overly dramatic character gets this when it looks like one of his allies has died, and he remains frozen, while the other characters, drawn normally, go about their business.
Of course, if you're as low on cash as the creators of Neon Genesis Evangelion were, you can make at least two entire minutes of plot out of nothing but Pastel Chalked (or Copic Marker) Freeze Frames.
Nodame Cantabile does these a lot during the concert scenes, of either Chiaki or one of the musicians during a dramatic piece of music. Probably just to vary a bit between these and pans over ordinary stills, when the time or budget for proper animation of the musicians runs out.
Dragonball Z absolutely loves to end episodes with this. Not so much in later episodes, though.
Berserk is fond of doing this for dramatic moments, usually when Guts is doing something particularly Badass.
The Pokémon episode "Arriving in Style!" uses this quite a bit. They seem to be using it for cool poses at the end of episodes or for dramatic effect during fights now. At any rate, its use is on the rise.
Rose of Versailles uses the "dramatic moments" variety of this trope. Constantly. Once again, directed by Dezaki.
Oniisama e..., as well.
Violinist of Hameln is the king of this trope. Due to an impossibly constrained animation budget—rumour has it the budget was mainly spent on obtaining rights to the classical music—the series sometimes seems to consist mainly of whole montages of one Pastel-Chalked Freeze-Frame after another. Within the fandom, the show has since gained the affectionate nickname "Slideshow of Hameln".
One of the many things Bobobo-Bo Bo-bobo plays with.
Many episodes in The Slayers end with these.
Tengen Toppa Gurren Lagann uses this. In addition, the Big Bad of the first arc, Lordgenome, is so badass that he exists in a constant state of Pastel-Chalked Freeze Frame. Except it averts the "Freeze Frame" part.
When Holy Roman Empire runs away from Italy during one rather suspenseful part of the Axis Powers Hetalia anime, there are several of these shown from different angles. The story was not continued until several episodes later.
Kenichi: The Mightiest Disciple does this whenever something awesome or dramatic happens. It's also played for comedy on at least one occasion when the moment is so dramatic it causes Kenichi to faint.
Sailor Moon employs these quite often. Haruka and Michiru in Sailor Moon S live and breathe this trope, taking it to Narmtastic levels when they use it several times an episode, usually to begin and/or end every scene they're in.
- Haruka and Michiru's scenes are done this way more often then not, when NOT in any form of battle, in order to emphasize how elegant they are or something
There is at least one in Sister Princess, at a climactic moment in the penultimate episode, although the moment is anything but an action shot.
Killer7 has a few of these during the level where all the cutscenes are done in anime style.
Otogi Zoshi uses these frequently.
Parodied in Ninin ga Shinobuden, when Onsokumaru fights himself.
Keroro Gunsou
- Parodied in the dub version of episode 8, when it prompts the narrator to ask who told the animators to switch to sepia.
- And in a later episode he asks if someone squirted grape juice in his eyes because everything's purple.
Lucky Star does this during the Initial D spoof, going from CGI to Pastel Chalked Freeze Frame as Yui executes the gutter-wheel turn.
Subverted in one scene of Naruto, where it looks like one of these happened at the end of an episode but when it zoom out you can see it just switched to a close view of a painting of that scene Sai made.
The Macross franchise has at least two.
- Macross Zero has one of Shin during the Final Battle in a dramatic moment just before he decides to jettison his weapons and charge in without violence in mind, hoping that the sight will snap Sara out of her Roaring Rampage of Revenge.
- Macross Frontier ends episode 24 with one of Sheryl Nome crying out in despair after she sees Alto's fighter explode.
Special A has pastel sections every single darn episode, usually when a character has just done something sweet and so "earned his watercolors".
Fushigi Yuugi does this at times.
Clannad
- The movie does this constantly. Even two in a row at times.
  - Guess who directed the Clannad movie. Hint: it isn't the same person who directed the TV series.
- Parodied in one episode of the series. Kotomi is putting on a violin recital, and though she hard practiced and greatly improved, she became nervous and her already next-to-non-existent violin skills are dropped back down to "deadly." All who are listening fall dead, one by one. As they fall, Pastel Chalked Freeze Frames are done for each of the fallen victims.
Happens at the end of every part 1 of any episode in Yu-Gi-Oh! 5D's, accompanied with "To Be Continued..."
The current page shot is Nicholas D. Wolfwood of Trigun, pictured in his second episode when he turns around and starts shooting the hell out of everything after a quickdraw competition he and Vash tricked each other into joining turns into a Vash hunt with child hostages. This is possibly the only use of the technique in the entire series, and it handily highlights the fact that Wolfwood is slightly nuts. Which you suspected all along, but by now you like him. It is to be noted he didn't kill anyone during said rampage, just put a lot of nonterminal holes in them. It is fortunate none of the abruptly-recruited bounty hunters had Gung Ho Gun levels of determination. The full line is: "I WON'T LET ANY MORE CHILDREN SUFFER! NEVER AGAIN!"
Several of these are used in the first episode of the Umineko anime during everyone's introductions.
The original Mobile Suit Gundam uses these from time to time.
- Alternate universes do it too. Dramatic shots of Exia charging with its sword drawn or Freedom in pose are particular favourites.

Fan Works

Lampshaded/spoofed in Yu-Gi-Oh!: The Abridged Series: "Oh no! The animation budget ran out!"

Films -- Live-Action

The Rocky movies end on an Acrylic-Painted Freeze Frame.

Live-Action TV

The Rocky example above is spoofed in Scrubs—J.D. and Turk keep fighting to prove their manliness. They realize that they won't be able to settle it. They have a flash of inspiration, and wind up taking a photo of them both in boxing gear, and each telling the story of how they won.

J.D. & Turk: (together) Rocky 3 freeze-frame ending!

Video Games

In Bayonetta, each time a new enemy type appears (including bosses), a mini cutscene plays with one of these and the name of the enemy.
The "Chapter Complete" bits in Eternal Darkness end like this.
The opening for Tales of Vesperia uses this before it fades to black and goes to the start screen.
Valkyria Chronicles inverts this by starting off with a sketch that begins to move. The entire art style of the game emulates a pastel chalk drawing.
Done with each To Be Continued screen in Asura's Wrath, just to make the parallels to be an interactive anime even more obvious.

Web Animation

Spoofed, appropriately enough, in the Strong Bad e-mail "Japanese cartoon".

Western Animation

The ending of the Family Guy episode "The Cleaveland-Loretta Quagmire" ends in a Pastel Chalked Freeze Frame with the Rocky theme Eye of the Tiger playing. The scene leading up to the freeze frame is verbatim of the final scene of Rocky III (see above).
Some of the action shots in Ben 10 are replaced with slowly-sliding comicbook-like images. Its sequel has yet to use this effect, presumably trying to move away from the more light-hearted nature of the original.
In Avatar: The Last Airbender, a bunch of these in a row were used to great effect in Book 1, Chapter 10. This is also how a fight between Azula and Suki ended, with Suki's fate not discovered until next season.
The Episode "Deep Six" of Teen Titans ends this way.
In Wakfu, it is used during the two 3-episode Gobbowl arcs, specifically as a Shout-Out to Space Adventure Cobra.
Several episodes of Thundercats, including the multi-part Anointment Trials.