Thanks for the input!

Swagmuffin, I agree with a few items and disagree on others; either way, thanks!. I'll make some changes to the guide based on your input. Below is the TL;DR version:

• Void Staff vs. Abyssal Mask: Runes, Athene's, and Merc Treads give you enough MR already, so this item is all about the magic pen. With the heavy nerf to Abyssal's aura, the flat magic penetration wouldn't hit for any of Veigar's spells at max range. The Void Staff is too important for dealing with enemies building MR.
• Frozen Heart vs. Zhonya's Hourglass: If you're absolutely sure that you'll have the blue buff before teamfights break out, I agree with you: Zhonya's is better than a FH on Veigar. I still have to stick with FH in general, though. The CDR is just too important to risk entering a teamfight without it.
• Warmog's Armor vs. Rylai's Crystal Scepter: 1270 health on a fully stacked Warmog's blows away the 500 health Rylai's offers. However, if you never seem to be in danger of dying during teamfights, the utility from Rylai's slow is amazing, and I agree: grab that instead.
• Rabadon's Deathcap vs. Rod of Ages: I've already built tons of health and mana elsewhere, and Rabadon's is core on Veigar.
• Sorcerer's Shoes vs. Mercury's Treads: Early-game, Sorcerer's Shoes are better, but once you've built a Void Staff, they're less useful. Merc Treads offer more at that point.

Harmander, I hope this convinces you that the build is solid. Thanks for the encouragement!

Mikuroo, thanks for the helpful criticism.

• You're absolutely right about magic pen percentages not stacking additively. I now know they stack multiplicatively, so that means the 50% should be (1 - 0.1)*(1 - 0.4) = 54% reduced MR, or 46% magic penetration. I'll fix that.
• I've re-thought the armor seals, and I agree: Veigar needs more mana regen early-game before he's built Athene's Unholy Grail. The build will now use Greater Seal of Replenishment.
• I didn't mean to make it sound like catching the carries is easy to do. I'll adjust the language in the Teamfights section.
• Yeah, 150 AP from Baleful Strike is pretty low. :P I was going for a conservative, low estimate to show that you don't even have to do that well in lane for this build to be viable. Granted, you're probably right--I'm not that good (1250 ranked) and do need to work on last-hitting!

Thanks again, everyone!

heres several things

Its not 50% btw, percents do not stack.

You have no mana regen masteries/runes/items to begin with, veigar already has one of the worst laning phases from 1-5, you are just making it worse :o

You say "simply find the adc or ap carry and nuke them"
well you can't do that cause veigar has no mobility and if you are playing against a competetant adc he won't suck that much. Also, you don't mention using your e to shield your own adc.

you say you only have an extra 150 ap per game :O? work on cs xp

i agree with swagmuffin however i do like the fact that you're challenging the meta. I'll try it some time!

I have to tell u, make this guide with Ability Power tank items. Like ill tell u wat to build. Rod of Ages will help Veigar with his mana and health and still give him ability power . Rylai's Crystal Scepter will give u a decent amount of ability power and give u the health u need. Athene's Unholy Grail will give u a good amount of ability power along with some mana regen and magic resist. Abyssal Mask is a ability power item that gives u magic resist and still lets u have ap. Zhonya's Hourglass is my favorite item to build on an Ability Power champion. It gives u a ton of ap and lets u go in a stage where noone can do damage for 2 seconds. Of cousre u can build Sorcerer's Shoes and get that magic penetraition or if ur looking for more ap u can build a Rabadon's Deathcap which gives u double the ability power u have. :)