(victory state not shown-you'll have to find out yourself! [unless the battle ended in a DQ.])
http://www.smogon.com/forums/showthread.php?t=86428 DarkSlay versus Its_A_Random. 1v1 Singles, switch=n/a, one ability, 3 days dq, two uses of Recover/Rest and 5 chills, no items.
http://www.smogon.com/forums/showthread.php?t=86321 DarkSlay versus Wikey. 1v1 Singles, switch=n/a, all abilities, 3 days dq, two uses of Recover/Rest and 5 chills, items enabled.
http://www.smogon.com/forums/showthread.php?t=86363 Engineer Pikachu vs. Rolf. 2v2 Singles, switch=KO, all abilities, 3 days dq, two uses of Recover/Rest and 5 chills, no items.
http://www.smogon.com/forums/showthread.php?t=102316 DarkSlay vs. Kaxtar. 2v2 Singles, switch=KO, one ability, 3 days dq, two uses of Recover/Rest and 5 chills, no items. Ended in DQ after the first round.
http://www.smogon.com/forums/showthread.php?t=86485 Deck Knight vs. Its_A_Random. 2v2 Singles, switch=KO, one ability, 3 days dq, two uses of Recover/Rest and 5 chills, no items. Notable for being the third-longest match in CAP ASB history.
http://www.smogon.com/forums/showthread.php?t=3446704 Banryu vs. Temperantia. 6v6 Triples, switch=KO, all abilities. 3 days DQ for battles, 5 days DQ for ref, three uses of Recover/Rest and no chills, no items. Additionally, all Pokemon on the team must have a combined rarity of 20 or less. Ended in a mutual forfeit.
http://www.smogon.com/forums/showthread.php?t=3448031 Spenstar vs. Objection. 1v1 singles, switch=antidisestablishmentarianism, one ability, 1 day DQ, no recover/rest/chill limitations specified, no items.
http://www.smogon.com/forums/showthread.php?t=103628 Galladiator vs. Solstice. 3v3 Singles, switch=KO, all abilities, 5 days dq, no uses of Recover/Rest and 5 chills, no items. The longest battle in ASB history-unfortunately primarily due to poor reffing habits.