Originally Posted by TealNinje
An enemy having Thornmail means they don't have Omen or Heart. This is why Tryndamere loves the item. If they DO have Thornmail AND Omen or Heart, they've spent a huge amount of gold on countering Tryndamere, and he can dedicate his teamfight presence to the other 4 members of that team. Especially if they have Omen; an enemy who has Omen is very dangerous for Tryndamere, but if that enemy is also one he has to kill early then it makes his life miserable (like a ranged carry or Xin Zhao/other burst AD). If they have Thornmail AND Omen, then he simply doesn't care about that target; they've used up 40% of their item slots and 5000+ gold to counter him, and he can just target someone else.
And if, by chance, they decide on Thornmail and some HP/offense item instead, f'rexample Rylai's/Mallet? Suddenly they're guaranteed to outlast Tryndamere, because their physical EHP is definitely higher than his magic EHP; the damage from Thornmail alone will deal a ton of damage, let alone the champion's innate skills/DPS. Now Tryndamere needs to spend money on MR so he doesn't murder himself targeting a mage who deviated slightly from their core build for a 2k gold Armor item.
I'm not debating that Heart or Omen aren't better, but that Thornmail is a solid item.
Specifically, it's good on mages and/or melees, because they're less likely to be able to afford Omen in their build; Frozen Heart is another matter regarding some mages, though it's far more likely to be something the team's tank builds.