Relatively Straightforward Items not in the Game yet.

1: Life Steal with Defensive Stats. (350 HP, 40 armor, 20% life steal)
1800g = Cloth Armor + Vampiric Scepter + Ruby Crystal + 575g

2: Ability Power with Defensive Stats. (425 HP, 60 armor, 65 AP)
2550g = Ruby Crystal + Chain Vest + Blasting Wand + 495g

3: Mana, Ability Power, Crit, and a Passive "Crit to Spells". (300 mana, 35 AP, 20% crit, Spells Can Crit doing 1.5x the damage - percent is equal to the player crit%)
2800g = Amplifying Tome + Cloak of Agility + Sapphire Crystal + 1085g

4: Crit, Attack Speed, AP. (15% Crit, 40% Attack Speed, 35 AP)
2400g = Recursive Bow + Brawler's Glove + Amplifying Tome + 515g

An upgrade to boots, all tier2 boots, that allows for the user to teleport to towers. Increases towers defenses considerably. 8 second cast. 1200g upgrade cost. (no other stats increase)

You could probably just recode blue pill to be targetable to towers. Probably easier than going through and making items "clickable"

HP -250
Dodge chance +20%

There are lots of ways you can use negative values to heavily change the worth and excitement of an item. Try making it a relational tradeoff. HP for AP is probably not as balanced as HP for HP Regen.

Another odd one since you mentioned boots. How about boots that increase your movement speed as long as you're going towards the enemy base. Not an easy one to code I imagine, and not a very good item all-in-all... but it's different and might spark some ideas in others' minds.

If they could only be used by tanks, sure. But we really, really don't need AP/tanking items to give casters heavy survivability as well as incredible damage. They can already manage that too well with the current item selection.

One item type missing is AP/Crit. This could be good for any number of casters that can make use of autoattacks, or anyone with a lich bane. (Or physical attackers could benefit, like Alistar with his fairly good AP abilities and ability to make use of autoattacks as effective damage.)

You will probably laugh at at this But I want a Cow!

YES a COW!

what it does: Heals a large amount of HP over time but you are slowed while you're affected by regen(seriously try eating a whole COW) AND it can also be used to Clear the brushes or trees, to play defensively while laning. But after you eat it,or it has eaten the brushes, its gone though and you can only carry one if that's ok. it's hard to carry 2 cows TBQH.

Edit:
"Cow" will be used primarily for it's terrain changing ability, Just like Tango in dota even though it can be used as Heal, it can be also used for creating indents, facilitating jungling, creating juke point and traps if you are Pude(will be useful since a pudge like character is on the way)

We desperately need a low to mid-tier crit/damage item.

What . . . the . . .

A counter item to dodge. +hit chance. As of right now, there is no counter to it, and its rather ridiculous trying to take out a dodge stacking jax whose also picked up a warmog's. Cant caster him down he has too much health, cant melee him down, you cant hit him. Make it cost about the same as +dodge items, or even make variants of the current dodge items that have hit chance instead of dodge.

Counter to dodge would be amazing, I have to agree. Jax is immortal if you don't have enough magic burst damage.