A couple of "No No's" that unfortunately made me dislike this guide:
-Tear of goddess is an early game item and should NOT be bought mid/late game.
-Fiendish codex before boots of speed is also very bad since veigar really needs that little extra movement speed at early game.
-I'd much prefer 9/0/21 before 21/0/9 mostly because of "Runic affinity" and "Meditation"
-Zhonya's should be an optional item vs heavy ad team

Hey!

Credits:
Your guide looks nice, the layout is nice and you didn't make to much text so it is apealing to read.

Constructive critism:
I have played my fair shares with veigars in a team, and the veigers that i have seen roling nicely are those who survived. A dead mage is no strong mage no matter how much ap. Your items work nice for Veig early-mid game or in fed games (wich actually also never make it to late game) but as soon as the big teamfights are going to start, your going to be focused and zhonias is not enough then since they have just 2 sec extra to plan how to kill you since you can't for example shunpo or any other escape like other champs do. Therefor I think zhonias could work on veig but should be optional vs heavy ad teams (cuz of the 100 armor on it) and in the stock build i would replace it with ROA.
Also i kinda miss the part about why not having a lich bane in your optional items list, lich banes effect can be devastating on veig since his attack range is 525, and his stun range is 650, wich gives you enough time to land 1 auto attack. Your veig build purpose is to nuke. Wich is possible with this setup but you can burst 500 dmge extra with 1 item. Seems viable imo (and it ads other great bonuses e.g. mspeed / ap and others)

I won't vote you up or down, this guide needs work, thats all.

GL!

Nice build. Pretty standard stuff. Madred's is a must but missing survivability. +1

So, how is Ignite ?

And I think if u wanna against strong damage team, should go for Rod of Age instead of Void Staff.