The Game Grumps have a huge amount of material that is unreleased, half-recorded or completely lost, mostly from the Jon and Arin era that have never been released to their channel due to various reasons.
For starters, a few episodes (three according to Arin) of them playing Conker's Bad Fur Day were made, but were never released and continued upon because, as explained in the first Banjo Kazooie episode and the panel Egoraptor did at Shadocan, Egoraptor really thought the game was bad while Jon was upset because he highly disagreed, "but was slowly realising why" (though according to that Banjo Kazooie episode his opinion hasn't changed), so they weren't talking, had a really awkward dynamic and on top of that it was a dialouge-heavy game that started off really slow, so it was really hard to put funny dialouge on top of it, which was another reason Arin hated it: a dialouge-heavy game wasn't really the best choice for Game Grumps, and that was the same reason Secret of Mana wasn't
(initially) played through properly on the show. Arin called the experience depressing, and called Conker the worst game they had to play on the show.
The same goes for Demons Crest (the initial playthrough that is, which may of had more than one episode); Jon wasn't having a good day, Arin liked the game but he hated it and they actually got into an argument about it ("Blood was shed" as Arin put it.), and above that, the episodes lacked jokes. They later replayed it on the show from the beginning, to which Jon mentioned that when they first tried it he "didn't much like it", so he was giving it another chance and that he originally didn't approach the game with an "old-school mindset". It was mentioned by Arin in his aforementioned Shadocan 2012 Panel and their Yoshi's Island playthrough.
And as confirmed at Magfest '11 there was also an episode for Dino City they made but never released. Since Jon had already reviewed the game on his channel the commentary consisted of (possibly only) referencing his review.
Not to mention, some games like Link to the Past and Mega Man 7, and possibly others, were replayed and rerecorded as their first playthroughs were trial runs for the show to test out recording and things like facecam.
They also have some truly lost footage and audio. As revealed in episode #2 of Yoshi's Island, one of them was a planned two-hour session of Mario Party 4. They recorded the audio but forgot to actually record the gameplay footage, (though again, it would later be replayed on the show anyway). They said they might release the audio in the future to riff on, but that hasn't happened yet and seems a little less feasible now since Jon has since left the show.
And as revealed in episode #67 of Sonic '06 they recorded themselves playing Super Metroid but lost the footage as it was contained on Arin's computer which later died on them, a fiasco they announced weeks beforehand in their Wheel of Fortune playthrough which was made to make up for the lost Super Metroid episodes. They did want to play it again for the show and as revealed in episode #5 of Journey to Silius it was attempted, but the footage ended up being lost again.
Speaking of Sonic '06, some footage of that game was lost partway through so they had to start their playthrough all over again. Nickelodeon Guts also had to be replayed because of the original playthrough's capture failing and four hours of Castle Crashers audio was lost because of another computer malfunction of Arin's: his laptop getting a blue screen of death, which was used for recording the audio.
Two unknown cases are the original playthrough of Strider 2 and a possible Sonic Adventure 2 episode. They may have done an episode on Sonic Adventure 2 because, as said by Arin on Twitter, after Arin said he hated the Sonic Adventure series with a lot of controversy following it he replayed it with Jon who was (again) releasing it wasn't as great as he remembered. But it's unverified as to if they were recording that playthrough for an actual Game Grumps episode or not, especially since there was an similar fast-forwarded event during one of the episodes of Sonic '06, in which after they had discussed the game's quality earlier, Arin showed Jon Sonic Adventure 2 on the Dreamcast to show that the gameplay was similar, to which Jon agreed on. And for the original playthrough of Strider 2 they had lost the footage and tried to salvage it, to which Barry said it was unsalvageable. But because they make no reference to an original playthrough in the version they did end up uploading, it's not fully verified if the footage did end up appearing in the currently uploaded playthrough or not
It's also unknown if some of the 'lost footage' episodes are completely lost or have remaining audio like the original Mario Party 4 episode, but it's probably unlikely. And it's also unknown if anything not truly lost from this page will ever see the light of day, especially if it's from the original era because, again, the original "Not So Grump" has now left.
In early 2015, it was found that multiple episodes of Game Grumps, specifically Dan era, had been suddenly marked as private. It was stated by Arin on the Game Grumps subreddit that Maker, the studio behind the Polaris network which the show is a part of, had been preemptively marking videos private to avoid potential copyright strikes. After this, they mentioned in multiple episodes that they were not allowed to sing copyrighted music, which appears to have been done in each of the videos marked private by Maker. About a month after this was addressed, it was confirmed on Twitter by Kevin, the show's third and most current editor, that they were allowed to sing again. Two previously private episodes that were made public once again were 1001 Spikes Part 1 and King's Quest VI Part 14. Though some remained private, including Empire Strikes Back Part 2 and Shovel Knight Part 7.
UPDATE: As of 9th December 2013, the second pair of Grumps have started playing Super Metroid again on the show.