Happens within the show too - during Scenes from a Hat, the suggestion "Bad Choices For A Presidential Running Mate" comes up, and Wayne goes into Gary Coleman mode while standing beside Colin, who's presumably the "presidential candidate"... until Drew points out that Colin even resembles Mr Drummond from Diff'rent Strokes, elevating the intended reference.
There's also the time where Colin was "a hairdresser whose colleagues all phoned in sick" in Sound Effects, and apparently got so "stressed out" from working several "customers" at once that he slipped into his Enemy to All Living Things act. Drew waited till it was over to comment "looks like Colin has a thing against places where they cut your hair."
Perhaps the most well-known moment is Colin's Newsflash over himself. He can't see that he's providing a news flash over footage of himself in previous scenes...yet, when asked how the incident started, he claims, "It all started with a badly timed bald joke!" Everyone goes nuts. After Colin eventually guesses what it is, he suddenly chuckles when he realizes, "I said the 'bald joke' thing, too!"
What's with Colin's garish shirts, you ask? It's so that he never winds up interfering with the Chroma Key during Newsflash, that's what.
For the UK version, you have the live-action intro. Improv is about the acting and jokes without the props and costumes; the intro has the costumes and props, but without the actors.
One "Scenes From a Hat" suggestion was rejected state songs. Colin sang: "Come to Florida and die!" This joke could be interpreted in two ways: That old people move to Florida (likely what Colin was intending), or that Miami has a high crime rate. It's fridge brilliance because you probably wouldn't think of both interpretations on initial watch.
In the "Greatest Hits" about Vegas, Colin remarked that he had a bit of a headache, because he accidentally had his head stuck in a vice for three hours. Upon first watch, this is merely a funny, random throwaway line, until you realize that the film Casino had a scene featuring a character whose head was crushed in a vice. This makes the line all the richer, and ties it into the theme of that playing to boot.
When "Scenes from a Hat" brings up the suggestion "Things George W. Bush does when he's by himself", Wayne mimes playing with a Speak-and-Say kind of toy that says "Shall we play a game?" It takes on different meaning if you know that that's the exact quote from WarGames.
This "Hollywood Director" from the revival series starts with some mild confusion over whether Greg or Jeff is the captain of the plane. Granted all planes have the exact same controls on both sides for safety reasons, but the confusion may well arise from the fact that Jeff's the one on the driver's side.
The first new game of Whose Line has Colin and Ryan mimicking the Superman scenario of Kal-El being placed in the vessel leaving a collapsing Krypton. Ryan mentions something about making the pod out of sand, which seems completely random until you pay attention to the dialogue - he's referring to the Kryptonian nanotech in Man of Steel.
Aisha gets into a semantics debate with the guys on the subject of Adelaide, and Jeff remarks that Drew never would have bothered with all that. Explains why he never learned that Africa is a continent, really.
One game of "Hats" sees Wayne getting a thing that looks like some creature is coming out the side of his head. Later on, the "Newsflash" game uses footage from Basket Case, which is actually about a creature that was really someone's deformed and seperated conjoined twin!
One "Greatest Hits" has Colin declaring an "unusual pairing" of Lil Wayne and Luciano Pavarotti. Not so unusual if you know that both of them have done that dozens of times (Lil' Wayne on mainstream releases, and Pavarotti in his Long RunnerPavarotti and Friends concerts.)
The "World's Worst: Person to be a member of the armed forces" has one that may shock you. Given the nature of the show, one would expect one of the participants to make a joke about Drew Carey, but it never happens. Then you learn that Drew is a former Marine.