I recently joined GameDev.net. Lots of good discussion there and good resources for new developers. The following's a carryover of my comments there.
Recordings of player moments (screenshots, video clips, etc) are great both in terms of player enjoyment and marketing. But a distinction should be made between planned and unplanned clips.
On the one hand, you have player-scripted events; machinima. Spore and The Sims 2 offer players in-game tools for this. Alternatively, World of Warcraft is commonly used but through external tools not provided by Blizzard. Such recordings are popular, but the planning and interface know-how required limits their user appeal.
On the other hand are unexpected events which the player discovers and wants to memorialize. Replay systems are more rare, but also, I think, more valuable. NCAA Football '08, for example, automatically records every play and allows players to select from those recordings events for permanent memory. That means that if something unintentional or unexpected excites the player, it can be recorded after-the-fact. The game also allows the player to view the event from different angles. Similar systems allowing cropping and editing, but the simplest systems have the broadest appeal.
Of the two kinds of recordings, planned and revisited, the latter appeals to more gamers. It is more useful for marketing as well, since the recorded events represent actual, unscripted gameplay which any player might hope for.
I wonder if there might also be occasional value in audio recordings. At this time, apart from music, audio in games is rarely worthy of memory. Undoubtedly, some game enthusiasts have favorite lines of dialog and such which they would happily preserve, but game audio is not dynamic enough to offer individual experiences -- the primary basis of personal recordings. How to make it so is worth consideration.