Hi! This is my very first build to post on mobafire.com, and I do realize it is quite an odd build for Veigar. Yes, I'm no expert in runes and masteries, so they're just messed up; however, I did lots of experiences on skill sequences and item purchases, and those listed above are the ones I have concluded to be the most effective. It's no use for ganking. Instead, it let you be Veigar whom no one desires to confront alone. You follow this build, and you will be the master of 1v1. In other words, you will be the best mid-taking Veigar. Whenever I played mid with Veigar, I have never lost my lane. The worst case was when my score was 0-0-0 'til the formation (2 top-1 mid-2 bot) was destroyed. So just give it a shot, and write a review or vote or do whatever you want!

Most of other builds for Veigar often masters in the order of Dark Matter, Event Horizon, and Blateful Strike. However, in my build, it masters in the order of Blateful Strike, Event Horizon, and Dark Matter -- which is exactly the opposite of what's usual. Although this may seem odd to you, I guarantee the effectiveness of this skill sequence; for your information, I have never failed in any kinds of 1v1 battles. I do admit that it is quite tough a task to slain a "tank" champion in 1v1 with Veigar. In spite of the fact, this skill sequence will deal a great damage to even those champions with superflous amount of health.
Since Blateful Strike has the fastest cool down, it is going to be used the most. That is why I master this the earliest. Its frequent use will be really helpful if the skill is strong. By mastering it, you are getting the most out of Blateful Strike everytime you use it, which is about less than 5 seconds.
Instead of mastering Dark Matter, I master Event Horizon first. This is to increase the accuracy of Dark Matter. Without long stun time of Event Horizon, it is pretty hard for Veigar to drop Dark Matter right on the enemy's head. Therefore, I thought that for the best success of Dark Matter, mastery of Event Horizon was REQUIRED. Also, long stun time of mastered Event Horizon will make it easier for Veigar to run away from other fast champions.
Although I master Dark Matter the latest, it does not mean I value it the least; once it is mastered, it deals great a damage on your foe. It's just that I don't think it's THAT needed to master Dark Matter since the early stages of the game. The reason why is what I call the "Full Attack Sequence." It's when you have all of your skills available and have enough mana to cast all of them. Veigar's Full Attack Sequence is [Event Horizon-Dark Matter-Blateful Strike-Ultimate-Deathfire Grasp-Ignite-Blateful Strike]. (If you have ever read descriptions of Deathfire Grasp (an item), you will realize that it can attack other champions, dealing the damage of 30% of thier health.) Even without the mastery of Dark Matter, masted Blateful Strike, Ultimate, Deathfire Grasp will almost kill your foe and Ignite will take care of your running away enemy.
I'm sorry if this was too long, but just try that skill sequence and you'll automatically understand what I'm talking about!

I value Deathfire Grasp as the most important item. That is why I start my build with Amplifying Tome. It increases your ability power by 25, and it is a necessary item for Deathfire Grasp. The reason DEathfire Grasp is important is that it gives you 60 ability power and it can be used to attack your foe (dealing damage of 30% of your enemy's health). I do not focus on buying shoes very much. I usually focus on ability power and health. Since Veigar's got Event Horizon, I never needed shoe that much; except for when my enemy is running away. That is why Ignite is also needed. I'll talk about it in the next chapter. Anyways, once I get Deathfire Grasp, I recommend purchasing Haunting Guise. It increases your ability power and also gives you 200 health. Veigar has a low health, and it will buy him some more time to get your enemy down when fighting 1v1.

Ignite: Most of other builds for Veigar recommend you ghost and flash. However, I think Ignite is more valuable -- when your enemy has only a little health left, and it is running away, you would not wanna waste your ghost or flash on chasing it; instead, you'll use Ignite on it and just go back to your turret and wait 'til it dies. And when you're running away, you will use Event Horizon (that's why I recommend mastering earlier than Dark Matter).
Teleport: It just makes your life easier. No one likes to waste their time moving from one side of the map to anther.