Tryndamere is one of League of Legend's melee carry-s, which means, indeed, that he becomes nigh-unstoppable lategame as he gets more and more items (though despite what you may think, Tryndamere is not nearly as powerful now as he was back near release)
Tryndamere's counter is hard CC. If you don't have CC (which is quite possible in blind pick), you have no real option other than to prevent him from getting kills in the first place.
This is, in part, why Tryndamere is considered something of a "newbie stomper" - without CC and coordination, both often lacking in newer players, he can be a royal pain to deal with.
The truth of the matter is that Tryndamere, like all carry-s, is fragile. Without his ult, he melts like paper, especially under focus.
What Tryndamere wants you to do, more than anything else, is stand still and let him crit you to death. So don't let him - use your CC to snare him, slow him, keep him at arms length. (I dare say you'd be hard pressed to find a team of 5 without one slow or better betwixt all of them)
The goal when fighting Tryndamere should be to get him to use his ult, then disable him for its duration, then kill him. If he uses his ult to flee, all the better - re-engage on a team fight within 2 minutes, and it'll still be on cooldown, making him prime to focus.
In terms of surviving Tryndamere, you want armor, and lots of it. A Thornmail will cause Tryndamere's massive crits to likewise sliver his own health, while a Frozen Heart will reduce his attack speed while providing you armor (and mana).