Unforgotten Realms begins every episode with a black screen with a message about "the following episode", which is accompanied by an announcer-type voice not-quite reading the message word-for-word. The white text has deviated further and further from what the voice says in later episodes. Variations have included "The following episode may or may not contain the word 'tiddly wank'", "The following episode did not care for the new Batman movie", and "The following episode will not have one of those 'the following episode' announcements at the start of it." Episode Nine actually doesn't have one, cutting immediately into the recap and title theme. But at the end, the familiar screen shows up to inform you that "the following episode is over"
Not to mention the various loading screens throughout the site.
Bonus Stage started having one consistently after its 75th episode.
Zero Punctuation has this with the last two frames of the end credits. Some times hilarious, sometimes not so much. Before getting an official title song, Yahtzee used music with a title or theme that was related to the game reviewed.
The opening for each video in Profound Moments In Left 4 Dead 2 changes slightly depending on which season the video is a part of. The poster shown at the very start, the music played during it, and the images of the Survivors the players are controlling for that season all change, the former two being the poster and intro music for the campaign in question and the latter just being the Survivors doing silly things.
In Deadly Space Action!, early episodes begin with "In the future, space consists of eight hexagons..." and a witty ending. This stopped about halfway through season one.