A problem I find common with Annie late game is surviving long enough for the 2nd, 3rd, or 4th volley of ability attacks. You can cut down half of your enemies health, double or triple stun them, but they end up killing you (especially true with Mundo). Sure, many guides recommend getting AP and/or Mana focused items, and it is true that Annie is hardly a tank. However, even with 400-500 AP, I find that fighting opponents who are tanks and have stacked Magic Resist has quite painful without any survival items late game, especially when tibbers becomes but a nuisance.
After some experimenting with various items, I find the following item build manages to increase the survivability of Annie considerably without sacrificing her power too much. (in one match, I covered for my team against 4/5 of the opponents team while scoring two kills during a retreat)
Sapphire->Catalyst->Banshee's Veil/Rod of Ages
Ruby/Sapphire->Tear->Archangel's Staff (the 2% Mana->AP conversion means you will still have 300 or so AP at the end)
Boots of Mobility/Sorcerers Shoes/Mercury Treads
Sage's Ring->Zhonya's Ring
Sage's Ring->Glacial Shroud->Frozen Heart (25% decrease in CD, highly recommended)
Warmogs/Rylai's Crystal Scepter/Innervating Locket (depending on how far you are in the game and needs, Annie is an epic farmer so Warmogs will benefit her. Cost isn't an issue late game as she can farm enough in 3 minutes if done right)
Magic Resist Build:
Guardian Angel/Quicksilver Sash (depending on Budget/need, prefer Guardian)
Force of Nature
Nashor's Tooth (the reason I don't recommend this is due to the AP advantage of Frozen Heart+Archangel Staff. Mana regeneration is not worth it compared to pure mana for Annie)
I usually pick Frozen Heart along with Guardian Angel.
Comments on any better ways to increase Annie's Survival are welcome as I'm not a high ELO player.