There are a few cards that regularly see play in both Mainboards and Sideboards that can very easily throw a rather large wrench in the Gameplan.
Grafdigger's Cage: A Kitchen Finks's greatest nemesis. It completely stops the combo in its tracks and must be dealt with immediately. If this card hits the table and you can't Tutor for that last piece of the combo on the stack, immediately Chord of Calling for a Qasali Pridemage or it's a solid no-go for the combo win.
Torpor Orb: Melira, Sylvok Outcast & Co.'s other great nemesis. This card also completely stops the combo in its tracks and must be dealt with immediately or it's Game Over.
Hushwing Gryff: Essentially a Torpor Orb with wings. While it doesn't see play very often, it is still just as dangerous and should be dealt with just as ruthlessly.
Anafenza, the Foremost: Also doesn't see the front lines too often. But if she ever hits the table, she must be removed.
Scavenging Ooze: All it takes is one for this thing to eat a Kitchen Finks as soon as it hits the Graveyard and not only is the combo broken, but you also don't get the Persist creature back. While not as dangerous as Torpor Orb - they will have to run out of eventually - it is still something to look out for. Abzan Midrange likes to keep a few of these guys in the Mainboard so watch out for them.
Rest in Peace: See Above. See a trend? If it hurts our Graveyard or ETB abilities, it must go.
Phyrexian Revoker: This annoying fellow stops all of our Sac engine's in their tracks. So put that Abrupt Decay to good use on this guy. The same can be said of Pithing Needle.
Liliana of the Veil: Another staple for Abzan Midrange as well as 8-Rack. She kills off necessary combo pieces early, and removes pieces from our hand. While she is much easier to get rid of, she should not be ignored.
Auriok Champion: While not dangerous at first glance, her ability essentially counteracts the combo kill. Every time a Persist re-enters the Battlefield, she will gain the opponent 1 Life just as they lose 1 Life, netting 0 Lifeloss. It should also be noted that she has protection from Black, so is not removable with Abrupt Decay. This makes her and her Sisters a very dangerous threat.
Leyline of Sanctity: An extremely effective combo-breaker that can appear before the game even starts. Worse yet, it's 4 CMC means that its safe from Abrupt Decay. While it is handled relatively easily with a Qasali Pridemage or a Zulaport Cutthroat, it is vital that this card is removed. If one appears and you can;t tutor for a Qasali Pridemage or Zulaport Cutthroat, pray you draw one up quickly or just go for the Infinite Lifegain Combo and hope they scoop.