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Any of you who do know me know that I like playing tanky champions. You'll also know that you'll read a lot of what I say in my guide in other guides because it is important. The truth of the matter is that it is not all about defensive stats; it's mostly about defensive stats. One might ask "doesn't that mean it's exactly the same?" No it's not. Yes, you should focus on having good defense, but you don't want your defense to be too good. The fact of the matter is that if you do nothing but stack health, armor, and magic resist you are virtually no threat to the enemy team. Since that is the case the enemies will always target you last (if they are smart). Why's that bad? It's because they'll attack your other teammates first, and that defeats the purpose of being a tank.
Let's summarize why being a super tanker is bad:
-Smart enemies will ignore you because you cause no significant damage
-Since you are being ignored they will go around you and attack your teammates instead
-Your teammates will die, and then you will be easy with all of them focused on you
-The purpose of being a tank is defeated
In other words too much of a good thing can be bad.
That's some good common sense. For example let us examine a Talon from the same game: He had one Shadow Dancer, a pair of Berserker Boots, and four Blood Thirsters. Early on this is pretty deadly in 1v1 situations, but later on he couldn't even stand up to one enemy. He had no defense and no armor penetration, so he was easy prey. Meanwhile they still run away from me because: A. I can take a beating because I have Ninja Tabi, Frozen Heart, and Force of Nature on top of my Defensive Curl
B. I can dish out damage to all of them with my AOE (Tremors) and I am hard to stop because of my tenacity bonus, I am also constantly regenerating health at a fairly high rate, so giving me a break just gives me an advantage
C. The said AOE also does decent damage and comes with a slow from Rylai's and Moonflair Spellblade adding to the base damage
D. Being near me is painful in general because I have the basic attack slow aura and Sunfire Cape as well as short cool downs on Power Ball and my Defensive Curl, which makes it hurt to even hit me (Rammus actually has a pretty nice AP ratio on his abilities)
That's a very scary Rammus if you ask me. He can charge into the middle of a fight with Power Ball and start channeling Tremors just as he gets near, applying some damage and an AOE slow, then use defensive curl to tank through their damage (probably their burst too) while still channeling Tremors, slowing all of them down and continuing to deal damage to them. Defensive curl will also give him a damage boost as well since his AD scales off of his armor value. After they see that and his team coming up behind him they will probably try to flee, which will be hard because Rammus is slowing them and can also taunt for up to three seconds to keep a priority target from leaving.
Fun Fact: When Tremors is maxed the maximum damage dealt is 1560 (+ 240% AP) over eight seconds. With this load out that brings the total damage done to all of the enemies, if they stand near you for the full duration, to 936 with 50% magic resist mitigation (this math was done with the simple numbers. I do not know if there are any other values I should be including). The chances are that the more damaging champs do not have that much damage mitigation and it will be well over a thousand. This ability's cool down is also so short that there's almost no drawback to spamming it whenever a team fight starts.
To sum up this guide so far: You should be intimidating. Leaving you alone would be a bad idea and the other team knows it. That is why they pay attention to you instead of ignoring you.
That leaves us with the question of how to do such a thing. Tanks don't have that much offensive ability, but there are many ways that you can increase your damage output enough that you are more than just a nuisance. Let's take Shen for an example: He needs high health for his bonus damage and sustain to begin with, but that doesn't mean you should get Warmog's Armor. If you use Rylai's instead you can slow enemies down with your Vorpal Blade, and it will also deal some decent damage. Your Shadow Dash will also do more damage and your Feint and Stand United shields will absorb more damage. To make a long story short the benefits of more AP and a slowing effect offered from having Rylai's Crystal Scepter outweigh the benefits that Warmog's Armor's extra health offers. It's not difficult to get over three thousand health without Warmog's Armor and it will last longer because of your shield spamming being so effective at soaking up damage. If we look at Rylai's by itself in this load with Feint maxed that's about 300 damage that you don't have to take. Feint is also very cheap, you can use it every five seconds (default cooldown), and it makes Ki Strike activate more often, which will restore more than half of the cost of casting Feint (30). If you suck up three hundred damage every five seconds then the gap starts getting pretty wide, but Shen is also somewhat bad at dealing damage. How can we make him better? The answer is more attack speed. Attacking the enemy more will cause Ki Strike to trigger more often, which restores your energy and deals extra magic damage. It can also benefit to play Shen with one or two hybrid items. A Hextech Gunblade gives him great sustain and makes his auto attacks even more of a pain, not to mention the ability power making his Vorpal Blade and Feint spamming more effective. Guinsoo's Rageblade also helps him take advantage of the Ki Strike because of the increased attack speed and his ability power can be ramped up further if you fight a little before hand. Suddenly Shen is slapping you around with his swords for both melee and magic damage and it is starting to hurt. The worst part of it is that when you try to run away he uses Shadow Dash to catch you and taunt you. Since Shen is still tanky there's not much that you can do about it unless you can make it painful enough for him to leave by yourself.
TLDR, in sum, and for those of you who are not fond of Shen: Do some research on your character's abilities and find out how to best utilize that character as if he was going to have an offensive focus, then strike a balance between offense and defense. This guide was brief, and you can find more information on effective ways to play your characters by looking them up on the Wiki or looking up guides for them around the internet.
Important Links, Characters, and Items:
League of Legends Wiki (http://leagueoflegends.wikia.com/wiki/League_of_Legends_Wiki)
Mobafire Strategy Guides (http://www.mobafire.com/)
Rammus, the Armordillo (http://leagueoflegends.wikia.com/wiki/Rammus)
Talon, the Blade's Shadow (http://leagueoflegends.wikia.com/wiki/Talon)
Shen, Eye of Twilight (http://leagueoflegends.wikia.com/wiki/Shen)
Rylai's Crystal Scepter (http://leagueoflegends.wikia.com/wiki/Rylai%27s_Crystal_Scepter)
Warmog's Armor (http://leagueoflegends.wikia.com/wiki/Warmog%27s_Armor)
Ninja Tabi (http://leagueoflegends.wikia.com/wiki/Ninja_Tabi)
Frozen Heart (http://leagueoflegends.wikia.com/wiki/Frozen_Heart)
Force of Nature (http://leagueoflegends.wikia.com/wiki/Force_of_Nature)
Sunfire Cape (http://leagueoflegends.wikia.com/wiki/Sunfire_Cape)
Moonflair Spellblade (http://leagueoflegends.wikia.com/wiki/Moonflair_Spellblade)
Hextech Gunblade (http://leagueoflegends.wikia.com/wiki/Hextech_Gunblade)
Guinsoo's Rageblade (http://leagueoflegends.wikia.com/wiki/Guinsoo%27s_Rageblade)