When I first started playing, in the open Beta days before Udyr came out even, Just seeing Anivia I was intrigued. Not knowing any mechanics, abilities, or even the basics of the game I felt that was the one, single, and only champion I would want. Saving all that IP didn't happen very quickly so didn't start with her; however, once I put some money into the game the deed was done and not once has even a shadow of regret appeared about any of it.
When Galio was announced I felt similar, but not quite. While a close second, Galio just does not give me the same feeling. Even after playing literally hundreds (probably about 1000 games) as Anivia alone, she is the one I always have, and always, will return to.
I play her very little now as everyone calls mid and I tend to just fill in, but she shall always be my beloved.
Starting out I never really used the wall, or built any tanky item, but the AOE capabilities and zoning abilities were so very enjoyable when even just fumbling around and learning. Now that I fully know how to, when to, and most importantly when not to utilize the wall, I find it to be probably the most unique and underrated ability by far.
And nothing, NOTHING, will ever be as fun as leveling again. Being sent top as Anivia, into a 1v2 lane because people buy WW and want to jungle. Having Sion + other dive minions, puting me into egg, but dieing before they can finish me off giving me first-blood double kill over and over again.
Still regret none of my 4 real pentas were obtained with Anivia, and that I don't get to play her much now, but there is a time for everything, and I know one day I shall return to her once more.