Here is a little theory crafting. As an AP Carry, you are first typically going to be laning against another AP carry. Champions in lower levels will have roughly 30 MR base unless they happen to rune for it, such as they desire a more passive farming lane. By getting Magic Pen Marks and Sorc boots, a common choice if you wish to deal more damage - no boots provide any AP, this will give you close to 30 MPen, which means that you get to do true damage as no damage will be mitigated by the champion's Magic Resist. This helps you win your lane.
Depending on the AP ratios of your abilities, the damage gained by building AP versus building MPen can vary.
Suppose you already have sorc boots and runes to get you 30 flat MPen with 10% MPen mastery. From runes+masteries you have 25 AP and just hit level 6 as Annie. You have gold and wondering between Needlessly Large Rod or Haunting Guise. Your opponent has 50 MR on them, so 20 MR effective after your MPen (or take 83% of your damage)
You have 1 pt in Disintegrate, 3 in Incinerate, 1 in Molten Shield, and 1 in Tibbers.
Note: Disintegrate has 0.7 AP Ratio, Incinerate has 0.75 AP Ratio, Tibbers has 0.7 AP Ratio with a 0.2 AP Ratio burn.
If you take the Haunting Guise, you'd have 50 AP, but do true damage with the MPen:
Disintegrate: 85 + 35
Incinerate: 180 + 37.5
Tibbers: 450 + 35 with 35+10 burn
Tibbers and 3 seconds of burn with full spell combo is 485+45*3+217.5+120 = 957.5 damage done
With Needlessly Large Rod, you'd have 105 AP, but they take 83% of the damage from MR:
Disintegrate: 85 + 73.5
Incinerate: 180 + 78.75
Tibbers: 450 + 73.5 with 35+21 burn
full spell combo is (523.5+168+158.5+258.75) * 0.83 = 920.2 damage done
So even with the extra gold spent to get Needlessly Large Rod and less health you get as Haunting Visage gives you 200 health as well, you end up with more damage done.
In summary, it varies on the situation and what the champions' AP ratios are. But you want enough MPen to nullify your targets' MR as much as possible. If the AP Champ has worse ratios than Annie, definitely favor MPen over AP. If the AP Champ has better ratios than Annie, then perhaps consider more AP. Of course, it always feels good seeing a large number as a stat for AP when you are playing the carry.