Attack Damage - Armor(mostly stuff like Thornmail or Frozen Hearts though of course there are many exceptions and items.)

Ability Power - Magic Resist(Negatron Cloak, Hexdrinker, Maw of Malmortius, Abyssal Scepter, many other items of course)

Burst Damage - Banishee Veil(This will generally throw off a person's entire burst combo considering you don't get hit by a skill before they start on it that is.) Another option is Guardian Angel's, if you plan on dying or being bursted down than this is probably best so you can rejoin the fight.

Being Focused - Zhonya Hourglass/Flash/Guaridan Angel

True Damage - More Health (not much more you can do with this.)

Invisible Champions/Wards - Vision Sight Ward/Oracles

(CC)Crowd Control(Stuns, silences, etc.) - Cleanse/Quicksilver Slash/Mercurial Scimitar/Mikael's Crucible/and items with tenacity such as Mercury Treads can be a great help in reducing the time of such Crowd Control.

Ganking - Wards of course! Though mia's or ss from other lanes are also nice to have. Or even the V to ping to fall back.

Counter Jungling - Either counter jungle back or place wards in your own jungle at main neutral camp spots, that way you and your teammates can catch them red handed and score a kill most of the time, as well as set back their jungling a bit.

Armor - Black Cleaver, Last Whisper(probably most effective overall since it ignores 35% of the target armor), Youmuu's Ghostblade, Brutalizer, and (optional) Blade of the Ruined King(which takes 4% of their hp away, doesn't reduce armor but its still quite nice to have overall.)

Magic Resist - Void Staff, Sorcerer's Boots, Haunting Guise, Liandry's Torment.

Healing Effect(s) - Ignite, Executioner's Calling.

(Pretty sure there are other thing's(in fact a lot) of things I'm forgetting but I guess this'll do for now, you're welcome to give your opinion's or even your own set of advice.

Well done. +1

To counter high-hp opponents, I know the Torment and the Deathfire Grasp both do % of current life damage. I think Blade of the Ruined King does as well (for those of you who don't need AP).

To counter healing effects, I know that Morello's evil tome did what executioner's calling did in Season 2. I'm a bit too lazy to check if it still does it now in Season 3.

They redid executioner's calling. It's pretty cool now. Grievous wounds is now passively applied to every autoattack instead of only applied by the active for a short duration.

Yeah, can't believe I left out an item such as DFG hahaha, but it yes indeed a good choice in countering opponent's with high Health, it also now gives 20% increased spell damage for 4 seconds to the target after its use.

I think Executioner's calling is much much MUCH more useful now than it was last season to be complete honest. You rarely seen people walking around with it maybe now we'll see more of it to counter those overly healing/lifesteal type champions.

This is defiantly not a bump. (sarcasm over the internet at its best.)