Options are limited for AP's, but it's even worse for AD champions IMO. I'm disregarding AD tanks and offtanks who have by far the wide number of health choices.
However, for pure-APs (such Annie), all you really need is RoA and Rylia's, combined costing 6140 gold. Those two combined have 1130 bonus Health and 160 AP. For comparison, a built Warmogs is 1270 HP at the cost of 3000 gold.
-On a different note, you can "increase" your health by choosing resistances like armor and magic resist. Frozen Heart, Abyssal Scepter, and Zhonya's Hourglass. Pick defensive items that can also boost your AP and/or CDR.