31 minutes in.
Nunu, 1-5-3 with 51 creep kills, waltzed into our base with 5 creeps and begins attacking the turret.
The only person in the base is Veigar, 9-1-5 with 92 creep kills. He was pretty fed.

Nunu and the five creeps, with Veigar unloading everything on him, killed our tower from 100% and escaped with 30% health.
This is working as intended, right?

Ya it's BS I just played a game with him and nothing killed him. He took over 10 turret hits and was still over half health at around level 11.

Not to mention his ultimate is ridiculous, even if you're barely on the outside of it you lose more than 50% of your HP.

Hehe, sounds like Nunu stacked some MR and probably had cleanse. It also sounds like Viegar got outplayed. Playing as Nunu I can usually live through a burst from Ryze or Veigar and generally just ignore them, or at worst consume a enemy creep as I continue beating on the tower. As long as you don't aggro the tower they really aren't much threat, so I would say yes, that is as intended. Not every character has to die to Veigar immediately, especially 31 minutes in.

I would absolutely love to see a screen shot of the equipment of that Veigar.

Here's what happened from what information you gave:

Nunu got slapped around a little bit early game. He goes and jungles, thus not getting **** for minion kills. Nunu then builds mass magic resist because your team is mage/ability spam heavy. He then promptly pushes because your team thinks he is going to be weak. Nunu then laughs at your team for assuming and wrecks your base.

Veigar was the only mage on the team.
Nunu had something like 4000 health and very little mana. You make it sound like Veigar pulls 1000 damage Balefuls and Meteors out of his ass 30 minutes into the game.

Thanks for even more information, got anything else left out?

As it is, it sounds like what I said happened still.

And no, not 1k's, 600s, before resists, and stuns to lock him? Yes.