Item Revamps (aka Things I Think Riot Should Do)
This is just an assortment of things I think Riot should look into or consider and some explanation as to why. Not much else to say about it, really.
THORNMAIL 
Currently, it grants 100 armor and reflects 30% of the physical damage dealt by basic attacks and abilities that apply on-hit effects. It's handy, but negated entirely by the immense burst offered by crit and the lifesteal physical champions build. It's all we have to stand up to crit burst, but it doesn't actually do anything to the champions.
I propose it be changed to start reflecting 10% of the damage. Every time damage is reflected within 1.5 seconds, a stack is added, up to 3, at which point it reflects 30% of the damage. In addition, starting at three stacks, reflected damage also applies Grievous Wounds in order to reduce the effect of lifesteal.
Alternatively, it could reflect 30% of the base damage, plus 50% of additional damage added by critical strikes from either physical or magical sources.
This makes it a minimal threat to champions like Caitlyn, who build crit, but also build serious damage, but makes it extremely dangerous to Ashe or Nocturne, who build speed and crit primarily. As it stands, it is the only defense against critical strikes that most tanks have and on average, it ends up not being enough. Thornmail should be something crit-based champions dread seeing on an enemy, not something they laugh at.
INFINITY EDGE and STATIKK SHIV

Infinity Edge is currently absurdly powerful and has replaced the Bloodthirster as a rush item for most carries. It currently grants a whopping 80 bonus AD in addition to its 50% increase to critical damage and 25% increase to critical strike chance. Statikk Shiv isn't in a much better place, being a rush item for most junglers. Granting 40% attack speed, 20% crit chance, 6% movement speed, and deals 100 magic damage to up to 4 targets, which can critically strike.
I propose we merge the two. Halve the damage granted by Infinity Edge and remove its passive, but keep the 25% crit chance. Halve the attack speed increase from the Shiv, but keep the movement speed increase and add a bonus 10 damage per level. Altering it so Thornmail reflected that damage as well wouldn't hurt. Rather than building out of a BF Sword, it could build from a Pickaxe, a Zeal, and an Avarice Blade.
Crit needs a serious rebalance as it is, but the additional damage from the Infinity Edge and the fact that it and the Statikk Shiv grant nearly 50% crit chance is entirely unnecessary.
TRINITY FORCE, PHAGE, AND FROZEN MALLET

A core item for any jungler and a handful of carries, the Trinity Force has been through quite a few changes. It currently grants 30 AP, 30 AD, 30% attack speed, 10% critical strike, 250 health, and 200 mana. One of its passives, Rage, grants 20 movement speed on baisc attacks, increased to 60 upon killing anything. Of course, it's halved for ranged champions, but that doesn't really help matters any. The other, Spellblade, has a whole 1.5 second cooldown, but deals 200% of your base AD as bonus damage. That's not an increase in damage to 200%, that's your full attack, plus 200%.
Phage, I was sad to see removed from the Frozen Mallet. I was disappointed when I saw Icy get taken away from it and even more so when I saw Rage. Granting 200 health and 20 AD, it's not that bad in its own right. It's the speed its passive grants that's unnecessary. Its passive is now identical in all forms to the Rage passive of Trinity Force, which means you could feasibly rush a Phage and never not be where you're needed.
The Frozen Mallet is one of my all-time favorite items and I absolutely hate to say I'm including it on this list. Granting 700 health, 30 AD, and a passive which reduces movement speed by 40% (30% for ranged champions) for 1.5 seconds on every single basic attack, you'd think it'd see a lot more action. Sadly, it doesn't.
I propose, much like the IE/Shiv entry above, that the items be merged. Remove Phage and give the Frozen Mallet its stats and place in the Trinity Force's build. With the removal of Rage, junglers could be convinced to build Furor boots. Junglers would lose no mobility and provide their team significantly more chances at getting kills. Since carries already build the Trinity Force, they could benefit from the chasing power it and Furor would provide. This would get the Frozen Mallet into peoples' hands again and stop Udyr from rocketing out of the jungle and decimating a lane all on his own.
These are just a few suggestions. I'm open to alterations on my ideas and general tweaking and I'd love to hear what other people think of the current item setup. This is a discussion forum, let's get discussing.